TOWARDS THE UNBOUND STELLAR POPULATION IN THESLOAN DIGITAL SKY SURVEY

By

Lauren Elizabeth Campbell

Dissertation

Submitted to the Faculty of the

Graduate School of Vanderbilt University

in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

in

Physics

May 2015

Nashville, Tennessee

Approved:

Dr. Kelly Holley-Bockelmann

Dr. Andreas Berlind

Dr. David A. Weintraub

Dr. David Ernst

Dr. Shane Hutson

To my family.

ii

Table of Contents

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Chapter

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1. Historical Perspectives on Galactic Structure . . . . . . . . . . . . 21.1.1. Stellar Halo . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2. Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.1.3. Bulge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2. Current View of Galactic Structure . . . . . . . . . . . . . . . . . 131.2.1. Bulge and Supermassive Black Hole . . . . . . . . . . . . 131.2.2. Thin & Thick Disks . . . . . . . . . . . . . . . . . . . . . 141.2.3. Stellar Halo . . . . . . . . . . . . . . . . . . . . . . . . . 171.2.4. Dark Halo . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.3. The Sloan Digital Sky Survey . . . . . . . . . . . . . . . . . . . . 321.3.1. Sloan Extension for Galactic Understanding and Explo-

ration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.4. The Unbound Stellar Population in the Milky Way . . . . . . . . 34

II. IDENTIFYING HIGH METALLICITY M GIANTS AT INTRAGROUPDISTANCES WITH SDSS . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.3. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.3.1. Testing the color selection region with real data . . . . . 472.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.6. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 52

III. HYPERVELOCITY STAR CANDIDATES IN THE SEGUE G & K DWARFSAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.3. Identifying HVS Candidates . . . . . . . . . . . . . . . . . . . . . 613.4. Estimating the Fidelity of Our Candidates . . . . . . . . . . . . . 64

3.4.1. Proper-Motion Quality Cuts . . . . . . . . . . . . . . . . 643.4.2. Monte Carlo Sampling . . . . . . . . . . . . . . . . . . . 67

iii

3.5. Orbits of HVS Candidates . . . . . . . . . . . . . . . . . . . . . . 693.5.1. Galaxy Model . . . . . . . . . . . . . . . . . . . . . . . . 693.5.2. Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.6. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.6.1. Chemical Tracing . . . . . . . . . . . . . . . . . . . . . . 723.6.2. Alternative Origins . . . . . . . . . . . . . . . . . . . . . 763.6.3. Follow-up Analysis . . . . . . . . . . . . . . . . . . . . . 773.6.4. Constraints on the Initial Mass Function . . . . . . . . . 77

3.7. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 79

IV. WORK IN PROGRESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.1. A Global Search for G/K-type Hypervelocity Stars . . . . . . . . 824.1.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 824.1.2. Candidate Selection . . . . . . . . . . . . . . . . . . . . . 834.1.3. Preliminary Results . . . . . . . . . . . . . . . . . . . . . 844.1.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.2. F-type Hypervelocity Star Candidates . . . . . . . . . . . . . . . 864.2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 864.2.2. Candidate Selection . . . . . . . . . . . . . . . . . . . . . 874.2.3. Preliminary Results . . . . . . . . . . . . . . . . . . . . . 874.2.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 88

V. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Appendix

A. ESTIMATION OF EXPECTED HVS VIA THE BINARY DISRUPTIONMECHANISM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

B. EXPANSION ON THE EXPECTED IGS CALCULATION. . . . . . . . . 99

C. IGS CANDIDATES REMAINING AFTER ALL CRITERIA CUTS. . . . 100

D. EXPANSION ON THE EXPECTED HVS CALCULATIONS. . . . . . . . 127

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

iv

List of Tables

Table Page

II.1. IGS candidates remaining after all criteria cuts [Complete version pro-vided in Appendix C]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

III.1. Stellar and kinematic parameters for the 20 HVS candidates. . . . . . . . 75

C.1. Complete and unabridged. . . . . . . . . . . . . . . . . . . . . . . . . . . 101

v

List of Figures

Figure Page

1.1. CMD of 47 Tuc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2. UV excess vs. Eccentricity, Velocity, and Angular Momentum . . . . . . 11

1.3. Density of F/G-type stars vs. Distance . . . . . . . . . . . . . . . . . . . 12

1.4. Schematic of Milky Way Structure . . . . . . . . . . . . . . . . . . . . . 12

1.5. Disruption of a Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.6. Galaxy Disk During a Merger . . . . . . . . . . . . . . . . . . . . . . . . 23

1.7. Galactic Disks of varying Heights . . . . . . . . . . . . . . . . . . . . . . 24

1.8. Evolution of a Clumpy Galaxy . . . . . . . . . . . . . . . . . . . . . . . 25

1.9. Number of Stars vs. Rotational Velocity . . . . . . . . . . . . . . . . . . 26

1.10. Metallicity of Disk Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.11. Stellar Density vs. Scale Height . . . . . . . . . . . . . . . . . . . . . . . 28

1.12. Mass Density of Disk Stars . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.13. Rotational Velocity of Stars with Metallicity < -2 . . . . . . . . . . . . . 29

1.14. Disruption of Satellite Galaxies into Streams . . . . . . . . . . . . . . . . 30

1.15. SDSS Map of Halo Structure . . . . . . . . . . . . . . . . . . . . . . . . 31

1.16. COBE Image of Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.17. Intracluster Light in Virgo Cluster . . . . . . . . . . . . . . . . . . . . . 36

1.18. Snapshot of Hills Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 36

1.19. Ejection Velocity vs. Kick Velocity . . . . . . . . . . . . . . . . . . . . . 37

2.1. CCDs of Covey et al. (2007) sample data . . . . . . . . . . . . . . . . . . 40

2.2. CCDs including L & T Dwarfs and SDSS Stripe 82 . . . . . . . . . . . . 43

2.3. Distinctions between M giants and M dwarfs . . . . . . . . . . . . . . . . 55

vi

2.4. CCD with M giant Standards from the BPGS Atlas . . . . . . . . . . . . 56

2.5. Comparison Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.6. Position of IGS Candidates vs. HVS . . . . . . . . . . . . . . . . . . . . 58

3.1. Transverse vs. Radial Velocity for HVS Candidates . . . . . . . . . . . . 62

3.2. Velocity Distribution for Most and Least Bound HVS Candidates . . . . 73

3.3. Comparison of Orbit in Spherical and Triaxial Halos . . . . . . . . . . . 73

3.4. Orbits of 7 Most Unbound HVS Candidates . . . . . . . . . . . . . . . . 74

3.5. Metallicity Distribution of HVS Candidates . . . . . . . . . . . . . . . . 81

4.1. Positions of Preliminary Global G/K-dwarf HVS Candidates . . . . . . . 89

4.2. Transverse vs. Radial Velocity of Global G/K-dwarf HVS Candidates . . 90

4.3. Velocity Distribution of Global G/K-dwarf HVS Candidates . . . . . . . 91

4.4. Metallicity Distribution of Global G/K-dwarf HVS Candidates . . . . . . 92

4.5. Velocity Distribution of Preliminary F-dwarf HVS Candidates . . . . . . 93

4.6. Metallicity Distribution of Preliminary F-dwarf HVS Candidates . . . . 94

vii

Chapter I

INTRODUCTION

In this dissertation, I present my work to identify and understand the unbound stellar

population within our Milky Way using data from the Sloan Digital Sky Survey. This

investigation is a single facet in the broader field of Galactic structure research. As I

will elaborate on in this document, this unique population can help us understand the

dynamics and stellar content of the Galactic center, the mass of the dark matter halo,

and the evolution of the Milky Way.

The study of Galactic structure isn’t simply compiling a map of the different compo-

nents that comprise the Milky Way. While this is important in itself, it is only the first

stepping stone to creating a complete understanding of galaxy formation, star formation,

and the distribution of dark matter through the Universe (Rockosi et al., 2009). Study-

ing the density, kinematics, and chemistry of stars and their preferred locations within

the Galaxy introduces new possibilities for understanding the formation and evolutionary

histories therein (e.g., Freeman & Bland-Hawthorn, 2002; Rockosi et al., 2009; Schonrich

& Binney, 2009).

To place this work in the context of Galactic Astronomy, I need to first provide some

background information. It is the goal of this chapter to paint a picture of our current

understanding of the structure of the Milky Way and how that view has changed over

time. To that end, I will begin, in Section 1.1, with a description of Galactic structure

as it was roughly 20 years ago and then move to a presentation of our current perception

1

in Section 1.2. In Section 1.3, I will discuss the Sloan Digital Sky Survey and how it

has had a tremendous impact on our understanding of Milky Way structure. Finally, in

Section 1.4, I will discuss ways in which understanding the unbound stellar population

can provide further insight into the larger context of Galactic structure, formation, and

evolution.

1.1 Historical Perspectives on Galactic Structure

Astronomical studies focusing on the evolutionary history of the Milky Way only

became feasible during the 1950’s when theoretical and observational advances were finally

able to join structure, kinematics, chemistry, and age into a single context (Majewski,

1993). The first development linking these parameters into a single model of the Milky

Way, and perhaps the most influential, came in the form of the Eggen, Lynden-Bell, and

Sandage model, discussed in detail in Section 1.1.1 below (Eggen et al., 1962; Majewski,

1993). A very simplified view of the Milky Way consists of a bulge and disk surrounded

by a diffuse halo. The following sections will elaborate on this picture.

1.1.1 Stellar Halo

Before the 1990’s the Milky Way halo was believed to be spheroidal, slowly rotating,

and comprised of metal weak1 stars, [Fe/H] < −1 (Freeman, 1987). Its rotational velocity,

1The metallicity of stars, typically denoted as [Fe/H], is a measurement of the amount of heavy metals(that is, heavier than Helium) in a star’s composition. Metallicity is reported with respect to that ofour Sun. Therefore, stars are described as either having more (metal rich) or less (metal poor or weak)metals than the Sun. Metallicity is also a signature of age as higher metallicity implies a star was formedmore recently.

vrot, was measured to be roughly 40 km/s, with a velocity dispersion2 of σ ∼ 100 km/s

(Freeman, 1987). This halo follows an r−3.5 density profile (Freeman, 1987).

The globular clusters that are found in the halo are also metal weak with [Fe/H] < −1,

and with similar velocities, vrot ∼ 50 km/s and σ ∼ 110 km/s, to that of the halo

(Freeman, 1987). In addition, about 30 globular clusters were known to lie on retrograde

orbits with vrot ∼ −70 km/s (Freeman, 1987).

Globular clusters are believed to be some of the oldest objects in the Universe, and

therefore provide an ideal test-bed for the earliest stages of galaxy formation (e.g., Bin-

ney & Merrifield, 1998; Freeman & Bland-Hawthorn, 2002). Figure 1.1 shows the color-

magnitude diagram of the nearby globular cluster 47 Tuc. The sharp knee at a magnitude3

of ∼ 17 indicates the age of the cluster since the more luminous stars have evolved off

the main sequence4. Because these clusters are the oldest observable stellar objects, they

provide a lower limit on the age of the Universe and the timescale over which galaxies

form.

The Eggen Lynden-Bell and Sandage (ELS) model of 1962 (Eggen et al., 1962) de-

scribes the formation of our Galaxy from a protogalactic cloud of intergalactic material.

To summarize, a large cloud of rotating gas, about 100 kpc5 in radius, began its collapse

roughly 1010 years ago. From the collapsing gas the first stars formed into globular clus-

ters, and as the material continued to collapse more stars formed in a rotating, thin disk.

2Velocity dispersion refers to the range of velocities about the mean. Therefore, a small velocitydispersion means all stars in the system have roughly the same velocity.

3Magnitude is a measure of brightness. Greater magnitude values correspond to fainter objects, andlikewise smaller values correspond to brighter objects.

4The main sequence is a feature on color-magnitude diagrams running diagonally from bright and blueto faint and red. Stars that are fusing Hydrogen into Helium in their cores live along the main sequence.

51 kpc = 3× 1019 m.

3

After time enough for the first O and B type stars6 to fuse their core gas into heavier

elements and undergo supernovae eruptions that would enrich the remaining gas at the

end of their lifetimes, a second generation of stars began forming in the disk of the Galaxy

(Eggen et al., 1962).

This model was theorized in order to explain correlations between ultraviolet (UV) ex-

cess7 and 1) orbital eccentricity, 2) W velocity (perpendicular to the plane of the Galaxy),

or zmax (height above or below the plane), and 3) angular momentum in a sample 221

dwarf stars in the solar neighborhood (Eggen et al., 1962; Majewski, 1993). Ultraviolet

excess is a signature of very old, metal poor stars. A correlation between this and any

other stellar property may provide information about how these stars, and therefore the

Galaxy, formed.

The first correlation, between UV excess and orbital eccentricity, is shown here in the

top-left panel of Figure 1.2. This figure shows stars with large UV excess have highly

eccentric orbits although stars exhibiting less UV excess live in nearly circular orbits

(Eggen et al., 1962).

The second correlation is between UV excess and maximum distance above or below

the plane of the disk, zmax. Stars with little UV excess remain in or near the plane of the

disk. However, stars with high UV excess have a wider variety of zmax values, ranging

from 0 to 10 kpc, shown in the top right panel of Figure 1.2. These two correlations,

6The spectral classification of stars follows the sequence: OBAFGKM. In general, the most massive,hottest, and bluest stars are denoted as O-type and transition down to the least massive, coolest, reddestM-type stars.

7The UV excess, δ(U−B), of a star is measured in the ultraviolet-blue wavelengths of a star’s spectrum.It manifests itself in very metal poor stars that have few elemental absorption features in this region ofthe spectrum resulting in excess emission.

4

together, suggest that there is also a correlation between UV excess and the age of the

stars– more UV excess in older stars, less UV excess in younger stars (Eggen et al., 1962).

Finally, the third correlation, between UV excess and angular momentum, shown in

the bottom panel of Figure 1.2, suggests that older stars with more UV excess have smaller

angular momenta than the stars with less UV excess (Eggen et al., 1962).

The combined results of these data leads to a concise description of the first stars in

the Galaxy. These stars tend to live on highly eccentric orbits, can be observed at a wide

range of heights above and below the plane, and generally have low angular momenta

(Eggen et al., 1962). This new information made possible a complete theory of Galactic

formation that describes how these stars came to have their observed properties.

In this model, the Galaxy forms from a smooth, hot cloud of rotating gas. As the gas

begins to cool and collapse, stars begin forming in globular clusters. Then, with continued

cooling, the remaining gas begins rotating faster to conserve angular momentum and

collapses into a flat disk and central spheroidal component. Therefore, the stars formed

during collapse have highly eccentric orbits, although the stars formed from the gas in the

disk have more circular orbits. As those stars enrich the interstellar medium at the end of

their lifetimes, the newly formed, younger stars will exhibit higher metallicities and lower

UV excesses.

The stars used in this study were primarily chosen to be nearby, solar neighborhood,

stars due to their high proper motions. Therefore, this sample, and this model, neglects

metal poor stars on low eccentricity orbits (Majewski, 1993; Bond, 1970). Also, the ELS

model neither accounts for nor explains the number of retrograde orbits seen in the halo

of the Galaxy (e.g., Majewski, 1993; Larson, 1969; Yoshii & Saio, 1979). The ELS model

5

was first challenged by Searle & Zinn in 1978 who noted a range in metal abundances in

globular clusters independent of distances from the Galactic Center (Searle & Zinn, 1978)

and suggested that the halo was built over an extended period of time from ∼108M�

independent fragments (Searle & Zinn, 1978; Freeman & Bland-Hawthorn, 2002).

The subsequent Yoshii & Saio model (Yoshii & Saio, 1979) incorporated low metallic-

ity, low eccentricity stars and retrograde orbits by allowing a slower collapse of a clumpy

protogalaxy (e.g., Majewski, 1993; von Weizsacker, 1951; Oort, 1958) over several gi-

gayears. This model lends itself easily to the (perhaps, preferred) notion of a possible

tumultuous Galactic evolution due to a series of hierarchical mergers (e.g., Majewski,

1993; Tinsley & Larson, 1979).

1.1.2 Disk

The Galactic disk is flat, rotating at 220 km/s with σ ∼ 20 km/s, and comprised of

the majority (6 × 1010M�) of the stellar mass (Freeman, 1987). The disk also contains

relatively high metallicity stars, with [Fe/H] > −0.5 (Freeman, 1987). It has an overall

scale height 300-350 kpc and scale length 3.5-5.5 kpc (Freeman, 1987). A spiral arm

pattern was also discovered in the Milky Way in the early 1960’s. There are at least 4

arms beyond 3 kpc from the Galactic center, and each is roughly 2 kpc from the next

(Rougoor & Oort, 1960). In addition, there is a thin layer of Hydrogen gas also rotating

at roughly 220 km/s (Rougoor & Oort, 1960). This disk of gas is also known to “warp”

at the edges, rising roughly 700 kpc above the Galactic plane on one side and similarly

below the plane on the opposite side (Rougoor & Oort, 1960).

It was well known that the scale height of the disk varied with stellar population

6

(Mihalas & Binney, 1981). For example, young O and B stars lie very near the plane

within ∼ 50 pc, interstellar gas and dust have a scale height ∼ 100 pc, and old M stars

and white dwarfs have scale heights ∼ 500− 1000 pc (Mihalas & Binney, 1981).

In 1983 Gilmore & Reid used the photometric parallax of a sample of 12,500 stars

complete to an I-band (near-infrared) magnitude of 18, and all within ∼18 degrees of

the South Galactic Pole. With these data they applied exponential fits of varying scale

heights.

They show, in Figure 1.3, the spatial density of two subsamples of their stars (in the

magnitude range 4 ≤ MV ≤ 5 and in the range 5 < MV ≤ 6, correlating to F-G type

stars and G-K type stars, respectively) as a function of distance from the galactic plane.

The solid line depicts an exponential decrease with a scale height of 300 pc. This single

exponential no longer fits at distances greater than 1000 pc. Therefore, they fit a second

exponential, the dashed line, for stars with z > 1 kpc, corresponding to a scale height of

∼ 1500 kpc for both subsamples of stars (Gilmore & Reid, 1983; Freeman, 1987). Thus,

Gilmore & Reid introduced an additional “thick disk” component, convincingly unique

from the thin disk population, to the existing two-component, bulge-disk, model of the

Milky Way.

They propose an explanation for this apparently distinct population of thick disk stars,

comprising only ∼2% of the stars in the solar neighborhood, ∼ 109M�, as being Galactic

bulge stars that have felt the gravitational pull of the massive thin disk. This is largely

due to the chemical similarities this population of stars has with the spheroidal component

of our Galaxy (Gilmore & Reid, 1983).

This led to many models describing the formation of this “thick disk” population, also

7

referred to as “extended disk,” “high velocity disk,” or “flattened spheroid” depending on

the preferred formation criteria (Majewski, 1993). These thick disk models tend to fall

into one of two camps– “top down” or pre-thin disk, or “bottom up” or post-thin disk

(Majewski, 1993).

The “top down” models form the thick disk population prior to the formation of the

thin disk (Majewski, 1993). In these pre-thin disk models the thick disk is often treated

as a transitionary stage between the collapse of the halo and the formation of the thin

disk (e.g., Majewski, 1993; Larson, 1976; Gilmore, 1984)

The “bottom up” models typically involve some interaction or evolution of the thin

disk that results in the formation of the thick disk (Majewski, 1993). These models draw

from the idea that processes that can increase the velocity dispersion of, or kinematically

heat, the thin disk stars may contribute to the formation of a thick disk population that

is smoothly linked to the thin disk (e.g., Majewski, 1993). Thus, we would expect to see

gradients in age, metallicity, and kinematics within the disks, as older, metal poor stars

would have undergone more heating events. Three main heating mechanisms considered

in these post-thin disk models include 1) interactions with ∼106M� molecular clouds, 2)

disk instabilities such as spiral arms, and 3) interactions with fast moving, massive objects

like dwarf galaxies or supermassive black holes (Majewski, 1993).

The thick disk component contains stars with [Fe/H] < −1, and has a velocity dis-

persion roughly double that of the thin disk, ∼ 40 km/s (Freeman, 1987).

8

1.1.3 Bulge

The central region of the Galaxy is comprised of a spheroidal stellar bulge. These stars

are metal rich with [Fe/H] > −1 and rotate at ∼ 200 km/s (Freeman, 1987; Rougoor &

Oort, 1960). The bulge is slightly elongated and has a radius about 2.5 kpc (Freeman,

1987).

The idea of a central bar was first introduced in the early 1960’s based on observations

of non-circular stellar motions near the center of the Galaxy (Rougoor & Oort, 1960; de

Vaucouleurs, 1964). It was suggested to be roughly 3 kpc in radius and oriented at about

30◦ from our line-of-sight (Rougoor & Oort, 1960; de Vaucouleurs, 1964). However, the

bar wasn’t studied in detail until the 1990’s, and therefore refer to Section 1.2.1 for a

more detailed discussion of its properties.

At this point, the generally adopted idea of what components make up our Galaxy can

be described by the schematic shown in Figure 1.4. This cartoon representation shows

a large dark halo extending out to about 100 kpc, in black, and smaller stellar halo, in

yellow, each with the old, metal poor globular clusters distributed throughout, marked by

the filled reddish dots. It also shows a thin disk, light blue, surrounded by a puffy thick

disk, dark blue, with radii about 15 kpc. Finally, in the center of the Galaxy is a stellar

bulge, shown in yellow (Freeman & Bland-Hawthorn, 2002).

9

Figure 1.1: The color magnitude diagram of globular cluster 47 Tuc. The location of the knee directlycorresponds to the age of the cluster, estimated to be approximately 12 Gyr. (Image courtesy of MichaelRichmond at http://spiff.rit.edu/classes/phys301/lectures/mw size/mw size.html.)

10

Figure 1.2: Top left: Ultraviolet excess as a function of orbital eccentricity. This shows stars with agreater UV excess tend to live on highly eccentric orbits, whereas stars with less UV emission have morecircular orbits. Top right: W velocity as a function of UV excess. Also plotted on the right-hand verticalaxis is Zmax above the plane. Stars with greater UV excess exhibit a much larger range of possible Wand Zmax values. Bottom: Angular momentum as a function of UV excess, showing stars with more UVexcess have little or no angular momentum. (Eggen et al., 1962)

11

Figure 1.3: Left: The spatial density of stars as a function of distance away from the plane for asubsample of stars with 4 ≤ MV ≤ 5 (late F- to early G-type stars). The straight lines representexponential fits to the data. A single exponential no longer fits at distances greater than about 1.5 kpcintroducing the need for a second disk component. Right: Same as left, but for a subsample of stars with5 < MV ≤ 6 (late G- to early K-type stars). (Gilmore & Reid, 1983)

Figure 1.4: A cartoon depicting the major components of the Milky Way. The bulge is shown by thecentral circle in yellow. The thin disk is in light blue and the thick disk around it is shown in darkerblue. Surrounding the bulge and disks is the stellar halo in yellow. Finally, the dark halo is shown inblack and the globular clusters by filled circles. (Freeman & Bland-Hawthorn, 2002)

12

1.2 Current View of Galactic Structure

1.2.1 Bulge and Supermassive Black Hole

Although a bar in the central region of the Milky Way was first introduced in the 1960’s

(Rougoor & Oort, 1960; de Vaucouleurs, 1964) with the discovery of non-circular motions

in the center of the Galaxy, it wasn’t until the early 1990’s that it became generally

established that the Milky Way is a barred spiral. The existence of a central bar has

been confirmed by kinematic, photometric, and star count techniques (Lopez-Corredoira

et al., 2007; Morris & Serabyn, 1996). Its mass is ∼ 1010M�, extends roughly ∼ 5 kpc

from the center, rotates at about 200 km/s, and is misaligned with our line-of-sight to the

Galactic center at an angle of ∼ 45◦ (Lopez-Corredoira et al., 2007; Morris & Serabyn,

1996; Rougoor & Oort, 1960).

Recently, new constraints have been made on the properties of the supermassive black

hole at the center of the Galaxy. This is largely due to new precision radial velocity

measurements of the high velocity stars very near the black hole (Ghez et al., 2008).

Ghez et al. (2008) determined the distance to the black hole is 8.0 ± 0.6 kpc, the mass is

4.1 ± 0.6 × 106M�, and a radial velocity consistent with zero.

The central parsec around the supermassive black hole is an important region of inter-

est. In particular, the central density profile may serve as a simple test for the existence of

a central black hole (Do et al., 2009). Theory states that as the orbits of stars bring them

close to a central black hole, the star is destroyed and its energy is balanced by increasing

the density of the central region surrounding the black hole. This results in a “cuspy”

density profile, ∼ r−7/4, although in the absence of a black hole a flat or “cored” density

profile is expected, ∼ r−1/2 (Bahcall & Wolf, 1976; Schodel et al., 2007; Do et al., 2009).

However, studies are finding a significant lack of old, low mass, stars near the center of

the Galaxy, resulting in a flat, maybe declining, density profile of ∼ r−0.3 (Do et al., 2009;

Bartko et al., 2010; Schodel et al., 2007).

1.2.2 Thin & Thick Disks

The existence and current observations of the thick disk can be explained by a number

of formation theories. Understanding how the thick disk formed will help to constrain

theories of Galactic formation and interaction history.

One possible formation mechanism for the thick disk is through accretion of satellite

galaxies. The simulations of Abadi et al. (2003), shown in Figure 1.5, imply that the

majority of stars in the thick disk, ∼ 75%, are the debris of tidally stripped satellites. This

theory suggests that the thick disk formed completely independent from a pre-existing

thin disk.

The thick disk may have alternatively formed by the kinematic heating of the thin

disk through minor mergers. Villalobos & Helmi (2008) consider this thick disk formation

mechanism in their simulations of galaxy mergers. They merge satellites with ∼ 10% of

the mass of a host galaxy which already contains a disk, seen in Figure 1.6. From these

mergers they find that thick disks form with similar kinematics to what is observed in the

Milky Way (Villalobos & Helmi, 2008).

Another possible formation mechanism of the thick disk comes in the form of scatter-

ing, or radial migration, of stars due to asymmetric structures in the Galaxy such as the

bulge or spiral arms. One study that investigates this theory was performed by Schonrich

14

& Binney (2009). They used the chemical abundances of solar neighborhood stars and

their space motions to evolve their orbits and recover the signatures of both thin and thick

disks in the absence of any interactions with external objects (Schonrich & Binney, 2009).

A similar study by Bird et al. (2011) simulates the effects of a bar and spiral structure

compared to the effects of satellites on radial migration in disk galaxies. Figure 1.7 shows

the stellar distribution in the initial disks (top with scale height, zd = 200 pc, bottom

with zd = 400 pc) on the left, and the stellar distributions after 2.5 Gyr in isolation and

in the presence of satellites, center and right panels respectively. Although a bar and

noticeable spiral structure forms in the thinner disk, satellite interactions have a much

more pronounced effect on the migration of the disk stars (Bird et al., 2011).

A competing theory is that the disks formed in situ from a ‘clumpy’ distribution of

material as the result of a major gas rich merger (Bournaud et al., 2007). The simulations

of Bournaud et al. (2007) show, in Figure 1.8, in addition to a clumpy primordial galaxy

being required to form an exponential disk, the time it takes to form the disk from clumpy

material is much shorter than the time it takes spiral arms to disrupt a thin disk into an

exponential disk.

Carollo et al. (2010), in addition to providing support for the two-component stel-

lar halo, see Section 1.2.3, proposed an additional metal-weak thick-disk is needed to

accurately describe the thick disk stellar population. In this study, they employ the dis-

tribution of rotational velocity, Vφ, and fit a minimum number of gaussian curves to

sufficiently describe the data. As a result, they claim a metal-weak thick-disk is required

with Vφ of about 100-150 km/s and a peak metallicity [Fe/H] = −1.3, compared with

the ‘regular’ thick disk which has Vφ ∼182 km/s and a peak metallicity [Fe/H] = −0.8

15

(Carollo et al., 2010). This result is depicted in Figure 1.9, where the histograms represent

the number of stars with a particular rotational velocity, the red curves represent each

of the components used in the model, and the blue lines are the sum of all components.

The left panel shows the distribution for a subsample of stars 1-2 kpc above the plane in

varying metallicity bins. Similarly, the right panel shows stars in a distance slice between

2 kpc and 4 kpc. As shown by this figure, a single component is not sufficient to recover

the distribution of observed rotational velocities (Carollo et al., 2010).

In 2011, a new study has challenged the determination of the thick disk scale length,

believed to be roughly the same as that of the thin disk, ∼ 3 kpc. Bensby et al. (2011)

add the metallicity distribution of a sample of 20 outer disk giants, further from the center

than the Sun, to a sample of ∼ 40 inner disk giants, between the bulge and the Sun. They

then compare this to the sample of solar neighborhood stars of Alves-Brito et al. (2010)

where they were able to distinguish thin disk from thick disk populations based on their

metallicity determinations. What they found is a significant lack of stars with thick disk

chemistry at large distances. This can be seen clearly in Figure 1.10, where the left panel

shows the 40 inner disk giants, the center shows the solar neighborhood, and the right

panel shows the 20 outer disk giants (Bensby et al., 2011). In each of these panels the red

and blue lines show the metallicity distributions of the thick and thin disks, respectively,

as they were determined from the solar neighborhood sample (Bensby et al., 2011).

A mono-abundance study of the SEGUE G dwarf sample revealed that each sub-

population can be described by a single exponential function (Bovy et al., 2012a). This

is shown in Figure 1.11, where stellar density is plotted against vertical scale height for

sub-populations in bins of metallicity and alpha-abundance; the black line shows the total

16

stellar density. Hence, Bovy et al. (2012a) suggest that “thick disk” stars do not comprise

a distinctly separate component from the thin disk. Similarly, Bird et al. (2013) considered

mono-age sub-populations in hydrodynamic simulations of Milky Way-like disk galaxies.

Figure 1.12 shows the vertical mass density profiles for the mono-age populations in the

inner disk, Solar neighborhood, and outer disk, respectively. Each sub-population can be

described by a single exponential function. However, the composite of all sub-populations

to form the total vertical mass density profile requires a fit by two exponential profiles

(Bird et al., 2013)– apparently explaining the origin of the thin disk/thick disk dichotomy.

In summary, there is still much that is undetermined about the Galactic disk despite

that it is the dominant stellar component in the solar neighborhood. The idea that there

is a “thick disk” in the Milky Way is generally accepted. However, the nature, formation,

and even the exact definition of what constitutes the thick disk is the subject of much

debate.

1.2.3 Stellar Halo

In the previous section, the halo component of the Galaxy refers to a smooth stellar

halo hosting low metallicity globular clusters (Eggen et al., 1962). This component only

contains∼1% of the stellar mass, ∼109M�, in the Milky Way and has close to zero angular

momentum compared to the disk and bulge components (Morrison, 1993; Freeman, 1987;

Freeman & Bland-Hawthorn, 2002). Now, we know this metal poor stellar halo component

is riddled with substructure, and it is believed that it formed, in part, from the accretion

of small, somewhat evolved, metal poor satellite galaxies (Searle & Zinn, 1978; Freeman

& Bland-Hawthorn, 2002).

17

Carollo et al. (2007, 2010) added to the substructure of the halo by providing strong

evidence for a two-component stellar halo– an inner halo and an outer halo shown in Figure

1.13. These two halos differ kinematically, chemically, and in spatial density suggesting

that they formed from entirely different mechanisms. (Carollo et al., 2007, 2010).

The inner halo exhibits a small net prograde rotation of 0 to 50 km/s, large orbital

eccentricities, a metallicity peak at [Fe/H] = −1.6, and dominates up to distances of

about 15 kpc. The outer halo, on the other hand, shows a net retrograde motion of −40

to −70 km/s, low eccentricities, a peak metallicity around [Fe/H] = −2.2, and dominates

beyond 15 kpc (Carollo et al., 2007, 2010).

It is proposed that the inner halo formed from dissipational mergers (containing gas) of

low-mass clumps into higher-mass clumps. Then the nearly radial merger of the resulting

massive clumps resulted in highly eccentric orbits and star formation in the recently

merged gas created the higher metallicity stars. Whereas, the outer halo formed through

random dissipationless (gasless) mergers of low mass, low metallicity satellites (Carollo

et al., 2007). It is the random orientation of the mergers that help to explain the slight

retrograde motion observed in this region.

1.2.4 Dark Halo

In addition to the stellar halo component of the Galaxy as previously discussed, we

know now that a massive dark matter halo surrounds the Milky Way. Navarro et al.

(1997) have theorized that all dark matter halos follow the same density profile regardless

of halo mass. The profile follows r−1 at small radii, and r−3 at large radii (Navarro et al.,

1997).

18

Dark matter cosmological simulations predict that there should be many more dark

matter satellites surrounding the Milky Way than the number of dwarf galaxies that had

been discovered in the early 1990’s (e.g., Simon & Geha, 2007; Kauffmann et al., 1993).

This discrepancy has become known as the “missing satellite” problem. With the advent

of the Sloan Digital Sky Survey (SDSS, see Section 1.3) the number of satellite galaxies

around the Milky Way, and in the Local Group, has increased to about 50 (York et al.,

2000a; Simon & Geha, 2007). Although this does not solve the “missing satellite” prob-

lem, it does dramatically alter our understanding of the Milky Way’s local environment.

Membership determinations of satellite galaxies require reliable distances and radial ve-

locities (Freeman & Bland-Hawthorn, 2002). Given the intrinsic low luminosity of the

objects and the current limitations of our surveys (SDSS has only imaged ∼1/5 of the

sky), it isn’t unreasonable that many more dwarf galaxies within the Local Group simply

haven’t been discovered yet (Simon & Geha, 2007).

From this follows the idea that some of the satellites may be “missing” because they

have been disrupted by interactions with the Galaxy. This question was addressed by

Morrison et al. (2000) and the “Spaghetti” Survey. This survey was designed to map the

substructure of the halo from the velocities of distant giants8, and ultimately to determine

the fraction of mass in the halo that was accreted from satellites (Harding et al., 2001).

With this survey, in combination with modeling the orbits of the halo giant stars, they

were able to recover the stripped remains of accreted satellites in the form of long streams

surrounding the Galaxy (Harding et al., 2001). An example of this is shown in Figure

8Giant here refers to the stellar evolutionary stage that occurs after a star has fused all of its coreHydrogen into Helium. In this stage the accelerated fusion rate in the shells surrounding the core causethe star to expand and cool dramatically.

19

1.14, which shows the X-Y and Z-Y projections of three satellites after 1 Gyr, larger

points, and 10 Gyr, smaller points, through its orbit around the Milky Way (Harding

et al., 2001). Similarly, shown in Figure 1.15, images from the SDSS have uncovered a

“field of streams” throughout the halo (Belokurov et al., 2006a). Typically, the mass

of one of these streams will be in the range 107 − 109M� (e.g., Law & Majewski, 2010;

Harding et al., 2001)

Since the gravitational potential of the Galaxy is dominated by dark matter at large

radii, observations of the large tidal features in the halo can be used to constrain the

shape, mass, and orientation of the dark matter in the Milky Way (Law & Majewski,

2010). Law & Majewski (2010) model the Sagittarius stream in different Milky Way dark

matter halos, varying the overall shape of the potential. Axisymmetric halos are not able

to reproduce the observed positions and distances of the stream. However, they suggest a

triaxial halo with minor/major axis ratio, c/a = 0.72, and intermediate/major axis ratio,

b/a = 0.99, to explain the observed structure.

The current picture of the Milky Way consists of a central supermassive black hole,

surrounded by a somewhat box-shaped bulge. The majority of the stellar material is

concentrated in a thin disk, which also contains spiral arms and a thin layer of gas that

warps at the very edges. Encasing the thin disk is a diffuse thick disk population. These

components all exist within an inner, prograde, stellar halo, an outer, retrograde, stellar

halo, and a massive dark matter halo housing the extremely metal poor globular clusters,

streams, and satellite galaxies. An image of the Milky Way from the Cosmic Background

Explorer (COBE) satellite can be seen in Figure 1.16. The figure clearly shows the boxy

shape of the bulge and the thin disk. More difficult to discern are the diffuse thick disk,

20

thin Hydrogen layer, and halo material.

This picture, although significantly more elaborate that what was described in Section

1.1.3, is still evolving. The desire to understand the center, disk(s), halo, formation, and

evolutionary history of the Milky Way is the driving factor for much of on-going research

today. This is especially exciting with more and more data becoming available. The

Sloan Digital Sky Survey (SDSS; York et al., 2000a) is only one example of a large survey

dedicated to such topics. Its contributions are described in Section 1.3.

21

Figure 1.5: The disruption of a satellite over time seen edge-on with respect to the main galaxy (notshown). A significant fraction of the stars in the satellite contribute to a thick disk population. (Abadiet al., 2003)

22

Figure 1.6: The disk of a host galaxy during a merger with a satellite (not shown). Over time themerger causes the existing disk to thicken. (Villalobos & Helmi, 2008)

23

Figure 1.7: Left: Stellar distribution of galactic disks with different scale heights (zd = 200 pc in thetop panels and zd = 400 pc in the bottom panels). The disk in the bottom panels more closely resemblesthe Milky Way disk. Middle: The disks after evolving in isolation for 2.5 Gyr. A bar and slight spiralstructure form in the zd = 200 pc disk. Right: The disks after evolving under satellite perturbations for2.5 Gyr. Bars, spiral structure, and disk thickening occur in both cases. (Bird et al., 2011)

24

Figure 1.8: Face-on views of the evolution of a clumpy galaxy. The result is a spiral disk galaxy withcentral bulge and 2-component disk (not shown in this projection). (Bournaud et al., 2007)

25

Figure 1.9: Left: The number of stars as a function of rotational velocity in varying metallicity bins forstars between 1-2 kpc from the plane, with the combined model for the distribution of velocities depictedby the blue line. The red lines are the Gaussian distributions for each component in the model. Right:Similarly, for stars between 2-4 kpc from the plane. (Carollo et al., 2010)

26

Figure 1.10: The center panel shows the metallicity of solar neighborhood disk stars. Red points arethick disk stars, fit by the red line, and blue points are thin disk stars, fit by the blue line. The left andright panels show the inner disk (open circles) and outer disk (filled circles) samples, respectively. Eachis compared to the trends determined by the solar neighborhood sample. There is a distinct lack of starsfollowing the thick disk metallicity trend at distances greater than 9 kpc. (Bensby et al., 2011)

27

Figure 1.11: Stellar density versus scale height for mono-abundance sub-populations of SEGUE Gdwarfs. Each population can be described by a single exponential function. The total stellar density isrepresented by the solid black line.

Figure 1.12: Each colored line represents the vertical mass density of a mono-age population in theinner disk (left), Solar neighborhood (center), and outer disk (right). Each mono-age population canbe described by a single exponential function. However, the composite of all populations (black curve)requires two exponential profiles (grey dashed lines) (Bird et al., 2013).

28

Figure 1.13: The number of stars with [Fe/H] < −2 and Zmax > 5 as a function of rotational velocity,with the combined model for the distribution of velocities depicted by the blue line. The red lines are theGaussian distributions for each component in the model. The parameter k is the number of componentsused in the model. When k=1 the fit is not descriptive of the data. However, k=2 does much better atfitting the data with only slight improvement at k=3, signifying that the 2-component model is accurate.(Carollo et al., 2010)

29

Figure 1.14: The X-Y and Z-Y projections of three separate satellites, identified numerically in theupper-right of each panel, at 1 Gyr and 10 Gyr (larger and smaller points, respectively–although, difficultto distinguish) throughout their orbit. This figure shows the disruption of satellites over time into largestreams surrounding the Galaxy. (Harding et al., 2001)

30

Figure 1.15: A map of the sky as seen by SDSS images showing the structure of the halo. Circlesdenote the location of globular clusters and satellite galaxies discovered by the SDSS. Other structuresin this image include the Sagittarius, Orphan, and Monoceros streams. (Image courtesy of http://www.sdss.org (????).)

Figure 1.16: This image of the Milky Way was taken with the COBE-DIRBE (Cosmic BackgroundExplorer- Diffuse Infrared Background Experiment) satellite. The image shows the boxy shape of thebulge and the dust throughout the disk has a slight reddish color. Also shown are the diffuse thick diskand the spattering of globular clusters and satellites throughout the halo. (Image courtesy of Ned Wrightand gsfc.nasa.gov.)

31

1.3 The Sloan Digital Sky Survey

Large spectroscopic surveys help to map the structure of the Milky Way both spatially

and kinematically (Rockosi et al., 2009). Furthermore, measuring chemical abundances in

today’s stellar populations helps explore the star formation history of the Galaxy (Rockosi

et al., 2009). The Sloan Digital Sky Survey (SDSS; York et al., 2000a) is one such survey

that has proved itself pivotal in understanding galaxy structure and formation.

The third generation, SDSS-III, is a six year program that includes four surveys- BOSS,

MARVELS, SEGUE-2, and APOGEE. The SDSS-III surveys focus on the following three

themes: 1) dark energy and cosmology, 2) the structure, dynamics, and chemical evolution

of the Galaxy, and 3) the construction of planetary systems (Rockosi et al., 2009). See

Sections 1.3.1 below for a more detailed discussion of the SEGUE surveys.

Some of the Sloan Digital Sky Survey’s many contributions to date include (SDSS-III,

2008; Rockosi et al., 2009):

• Discovery of distant quasars beyond redshift of 6, revealing supermassive black holes

in the early Universe;

• Using weak gravitational lensing to map extended mass distributions around galax-

ies, demonstrating that dark matter halos extend to 200 kpc or more;

• Demonstration of substructure around the Milky Way, revealing new tidal streams;

• Large samples of white dwarfs, used to obtain an accurate luminosity function to

study the cooling of white dwarfs and estimate the age of the Galactic disk;

• Discovery of many new satellites around the Milky Way and M31, nearly doubling

32

the known number of Milky Way satellites;

• Discovery of stars escaping the Galaxy, revealing encounters with the black hole at

the Milky Way’s center.

1.3.1 Sloan Extension for Galactic Understanding and Exploration

The Sloan Extension for Galactic Understanding and Exploration (SEGUE and SEGUE-

2) surveys provide stellar parameters, kinematics, and metallicities of stellar populations

from the disk and inner halo to the large distances of the outer halo (Rockosi et al.,

2009). SEGUE-2 added an additional 140,000 stars to the sample size of SEGUE, to-

taling 380,000 stars, and doubled the number of halo stars observed in SEGUE (Rockosi

et al., 2009).

The stars targeted by SEGUE were selected to be largely thick disk stars within

10 kpc of the plane, while SEGUE-2 stars were selected to consist of halo stars with

distances greater than 10 kpc (Rockosi et al., 2009). The target selection for SEGUE-2

was predominantly inspired by the desire to study the transition between the inner and

outer halos occurring at roughly 15 kpc (Rockosi et al., 2009).

A sample of the science goals of the SEGUE/SEGUE-2 surveys includes: detection

and analysis of stellar streams in the inner and outer halos, improved estimates of the

mass of the Milky Way, determination of velocities of thick disk, metal weak thick disk,

inner halo, and outer halo components, and to provide constraints on models of galaxy

formation (Rockosi et al., 2009).

33

1.4 The Unbound Stellar Population in the Milky Way

Stars can become unbound through a variety of mechanisms. We see this, for ex-

ample, in galaxy cluster environments where violent interactions are common. Galaxy

harassment– minor perturbations over extended timescales (Moore et al., 1996), and tidal

stripping from in-falling galaxies (Mihos, 2004; Byrd & Valtonen, 1990) can wrestle stars

from the underlying potential and result in a population of unbound stellar outcasts. We

see these diffuse collections of stars, called intracluster light (ICL), abandoned to the

space between galaxies in large clusters, such as Virgo shown in Figure 1.17 (Mihos et al.,

2005). Anywhere from 10% − 70% of the total cluster luminosity may be comprised of

ICL (Mihos, 2003; Murante et al., 2004). Determining the fraction of cluster luminosity

contributed by the ICL provides insights into the assembly history and evolution of galaxy

clusters (e.g.; Napolitano et al., 2003; Feldmeier et al., 2004b).

In the Local Group, home to our Milky Way, which is devoid of major galaxy interac-

tions, the unbound stellar population is more likely generated by three-body interactions

(Holley-Bockelmann et al., 2005). The preferred method of ejecting stars, called the Hills

mechanism (Hills, 1988), involves a binary star system and a supermassive black hole

(SMBH). One of the stars is captured by the SMBH, angular momentum is transferred

to the companion and it is flung from the galaxy with velocities approaching 1,000 km/s.

Figure 1.18 follows the orbital trajectories of a pair of stars as they become disrupted

via the Hills mechanism. The ejected companions are called hypervelocity stars (HVS).

Semi-analytic models predict O(100) HVS as a result this mechanism (Yu & Tremaine,

2003). Alternatively, this same effect can be achieved with a single star and binary black

holes.

A recent simulation study showed that it is possible to boost stars to hyper-velocities

via binary disruption scenarios in the disk (Tauris, 2015), Figure 1.19. These disruption

scenarios involve a binary star system, located within the Galactic disk, in which the

more massive star undergoes a supernova explosion and its companion is flung from the

disk. Contrarily, previous works showed that the ejection velocity resulting from a binary

disruption mechanism is a relatively modest 300 − 500 km/s generating, instead, high

velocity runaway stars (e.g.; Blaauw, 1961; Leonard & Dewey, 1993; Napiwotzki & Silva,

2012). The frequency of bona fide HVS ejected from disk binaries with velocities ∼1,000

km/s is yet undetermined9.

The following chapters present initial steps towards probing the existence and origin of

the unbound stellar population in the Milky Way and how it fits in the larger framework

of Galactic structure, formation, and evolution.

9We perform a rough estimation of the expected number of low-mass HVS generated from the super-nova binary disruption mechanism in Appendix A.

35

Figure 1.17: Left: Image of the Virgo Cluster captured by the Digital Sky Survey. Right: Longexposure image of the Virgo Cluster from Mihos et al. (2005) revealing the faint intracluster light betweenthe galaxies.

Figure 1.18: Still of an animation depicting the Hills mechanism (Image/animation credit: AndreasIrrgang). Red and blue lines trace the orbits of a binary star system around a SMBH (grey). The redstar is captured into a tight orbit around the SMBH and the blue star is ejected from the system.

36

Figure 1.19: Companion star ejection velocity as a function of supernova-induced kick velocity. Coloredlines indicate results of the disk disruption simulations of Tauris (2015). The blue line represents themaximum ejection velocity of ∼ 1, 200 km/s, showing it is possible to eject G/K-dwarf HVSs from thedisk with velocities comparable to the G/K-dwarf HVs candidates of Palladino et al. (2014).

37

Chapter II

IDENTIFYING HIGH METALLICITY M GIANTS AT INTRAGROUP DISTANCESWITH SDSS

Here we reprint, in its entirety, work published in the Astronomical Journal, 2012,

Vol. 143, Article ID 128.

2.1 Abstract

Tidal stripping and three-body interactions with the central supermassive black hole

may eject stars from the Milky Way. These stars would comprise a set of ‘intragroup’

stars that trace the past history of interactions in our galactic neighborhood. Using the

Sloan Digital Sky Survey DR7, we identify candidate solar metallicity red giant intragroup

stars using color cuts that are designed to exclude nearby M and L dwarfs. We present

677 intragroup candidates that are selected between 300 kpc and 2 Mpc, and are either

the reddest intragroup candidates (M7-M10) or are L dwarfs at larger distances than

previously detected.

2.2 Introduction

A significant fraction of the stellar component of a galaxy cluster is not confined to any

galaxy. These stars between galaxies form luminous halos, called intracluster light (ICL),

with very low surface brightness that can extend out to several hundred kiloparsecs around

individual galaxies (eg., Abadi et al., 2006; Krick & Bernstein, 2007). The brightest ICL

38

is less than 1% of the brightness of the night sky (Mihos, 2003; Feldmeier et al., 2004b),

thus making a complete census of ICL very difficult to obtain. High resolution N-body

simulations estimate that ICL could comprise 10%-70% of the total cluster luminosity

(Mihos, 2003; Murante et al., 2004).

It is commonly thought that intracluster stars are caused by one of three main chan-

nels: 1) stripping from galaxies as the cluster assembles either via high speed galaxy

encounters, tidal shocking, or a rapidly changing galaxy cluster potential (Byrd & Val-

tonen, 1990; Merritt, 1984), 2) long-lived, low level cluster perturbations in the form of

“galaxy harassment” (Moore et al., 1996), or 3) tidal stripping within in-falling galaxy

groups (Mihos, 2004; Rudick et al., 2009). These processes will generate a stellar ‘debris

field’ that is highly inhomogeneous, with distinctly non-Gaussian velocities that reflect

an unrelaxed intracluster population (Napolitano et al., 2003). Thus far, ICL has been

identified via planetary nebulae (PNe) (Feldmeier et al., 2004b; Aguerri et al., 2005), Red

Giant Branch stars (Durrell et al., 2002; Williams et al., 2007), intracluster globular clus-

ters (Lee et al., 2010; Peng et al., 2011), and ultra-deep surface photometry (Feldmeier

et al., 2002, 2004a; Mihos et al., 2005).

The properties of ICL may provide insights into the accretion history and evolution of

galaxy clusters (Mihos, 2003, 2004; Napolitano et al., 2003; Feldmeier et al., 2004b; Conroy

et al., 2007). Although there is some debate about the role that tidal stripping plays in ICL

production, it is expected that ICL substructure is correlated with the dynamical state

of the cluster (Murante et al., 2007; Mihos, 2004). Since the vast majority of galaxies

reside in poor groups, rather than in large clusters, it is of great interest to determine the

fraction of unbound stars that reside in these environments.

39

Figure 2.1: Color-color diagrams of the Covey et al. (2007) sample data. Main sequencestars are marked with black dots, giants with red crosses, and supergiants with greencircles. Note that the reddest giants (M7-M10), identified by the black dashed regions,are isolated from the stellar locus. This figure is a theoretical demonstration that verylate M giants have the potential to be isolated in color space in the ugriz bands, andthese dashed regions are meant only to highlight the spectral types of interest and do notrepresent our color selection criteria (given explicitly in equations 1 and 2). In particular,we drop the u − g and g − r cuts because objects at these distances are likely too faint inthe u and g bands. The locus of sub-solar metallicity giants is generally indistinguishablefrom the dwarf locus, and thus not plotted here.

40

In the Local Group, ICL has not been observed, though deep observations and star

counts have revealed a “field of streams” (e.g., Belokurov et al., 2006b). These streams

have been detected out to 100 kpc and are bound to the Milky Way (e.g., Yanny et al.,

2000; Ibata et al., 2001). Similarly, faint streams have been detected in the outskirts of

M31 (McConnachie et al., 2009; Ibata et al., 2007). Given that the Milky Way and M31

are not yet interacting and may not even be part of the same dark matter halo, it is

more likely that Local Group ICL, if it exists, would be a product of a different process

altogether.

One of the more recent suggestions for ICL production is via three-body interactions

(Holley-Bockelmann et al., 2005). For example, stars can be thrown out from the galaxy

through tidal disruption of a binary star system by a supermassive black hole (Hills, 1988;

Yu & Tremaine, 2003); this is the most common explanation for ‘hypervelocity’ stars such

as SDSS J090745.0+0204507, with a galactic rest frame velocity of ∼ 700 km/sec (Brown

et al., 2005). During this process, energy and angular momentum are transferred from

the black hole to one of the stars in the binary. The second star loses energy and becomes

bound to the black hole while the first is ejected from the galaxy. This is expected to

occur at a rate of 10−5(η/0.1) yr−1, where η is the stellar binary fraction (Magorrian &

Tremaine, 1999).

Another three-body interaction that is likely to expel stars is a close encounter of a

single star with a binary black hole (Yu & Tremaine, 2003). This is expected to occur

at a rate of 10−4(η/0.1) yr−1 (Magorrian & Tremaine, 1999). In this case, the star gains

energy from the binary black hole and is flung out of the galaxy while the black hole orbit

shrinks (e.g., Quinlan, 1996; Sesana et al., 2006).

41

To become gravitationally unbound, stars must exceed the escape velocity of the

Galaxy, now estimated to be 500-600 km/sec (e.g., Smith et al., 2007). Semi-analytic

models predict that there may be approximately 100 hypervelocity stars within 8 kpc of

the galactic center if the binary stars have equal masses (Yu & Tremaine, 2003). However,

intragroup stars (IGS) may not be solely comprised of hypervelocity stars; they may still

be bound but on very large, highly eccentric orbits– this can increase the potential num-

ber of IGS. One way to get stars on such eccentric orbits is through three-body galaxy

ejections of satellites like Leo I (Sales et al., 2007; Mateo et al., 2008).

As a first attempt to probe for a population of intragroup stars, we develop a technique

to search for M giant stars in between the Local Group galaxies. In this paper we present

our technique for identifying candidate IGS from the Sloan Digital Sky Survey (SDSS)

by applying color, distance, and proper motion cuts. Section 2.2 describes our technique.

We present our results in Section 2.3, and we discuss possible sources of contamination in

Section 2.4. Section 2.5 concludes and discusses methods to confirm the candidates.

2.3 Methods

During its eight years of operation, the Sloan Digital Sky Survey (SDSS; York et al.,

2000a) obtained deep, multi-colored images covering more than a quarter of the sky. The

SDSS uses 5 optical bandpasses (u, g , r , i , and z ; Fukugita et al., 1996a; Gunn et al.,

1998; Hogg et al., 2001; Gunn et al., 2006) with magnitude limits 22.0, 22.2, 22.2, 21.3,

and 20.5, respectively. The DR7 data set contains 12,000 square degrees of images and a

catalog of over 350 million objects with spectra of 460,000 stars.

As individual red giant stars in M31 have been observed down to the SDSS magnitude

42

Figure 2.2: Left: Color-color diagram similar to Figure 2.1, including L and T dwarfsfrom Hawley et al. (2002). The region of color space containing our IGS candidates ismarked by the black rectangle. Blue triangles represent dwarfs, green squares representsupergiants, red dots represent giants, blue crosses and green stars represent L and Tdwarfs. The blue and green error bars in the bottom left corner are representative ofthe typical 1-σ error bars for L and T dwarfs, respectively. Note that late M (M7-M9)and L dwarfs also contaminate the space. Right: Same as figure on the left, using SDSSStripe 82 stars (filled triangles) to represent the spread in the stellar locus (the errors arecontained within the size of the point) (Ivezic et al., 2007) and 677 extinction-correctedIGS candidates (filled diamonds). The cyan cloud results from the sum of gaussian-distributed errors on each candidate, i.e. the darkest cyan region represents the mostprobable location of the data. Similarly as in the left panel, the cyan error bar in thebottom left corner is representative of the typical 1-σ error bars for each candidate.

43

limits (e.g., Zucker et al., 2007), intragroup red giant stars will be observable. Indeed, at

a distance of 300 kpc, all supergiants and roughly half of any giants would be detectable

in the r , i , and z bands.

We developed our technique using the synthetic SDSS and 2 Micron All Sky Survey

(2MASS) photometry (Covey et al., 2007) of flux calibrated spectra of solar metallicity

main sequence, giant, and supergiant standard stars (Pickles, 1998). With simulated

SDSS and 2MASS colors (Schlegel et al., 1998), we obtained a stellar locus to search for

giants or supergiants that are isolated in a ‘clean’ region of color space. These color-color

diagrams are shown in Figure 2.1. We choose solar metallicity standards to probe for

IGS generated by three-body interactions within the central regions of the Galaxy, as

discussed in Section 2.1.

Unfortunately, most supergiants and giants lie along the main sequence locus, and

would therefore be indistinguishable by SDSS colors. However, there is a small area in

each of the color-color diagrams, shown with dashed boxes in Figure 2.1, where the rarest

M giants (M7-M10) are isolated from dwarfs and supergiants of the same spectral types.

Considering the distances we are probing and the very red colors of these spectral types,

we restrict our color selection to the r , i , and z bands as follows:

2.1 < r − i < 3.4, (2.1)

1.3 < i− z < 2.2 (2.2)

Again, we drop the u − g and g − r cuts because objects at these distances are likely too

44

faint in these bands.

Since these objects are so red, they may be confused with other nonstellar objects1.

However, we find that even quasars with z > 4.6 are too blue in i − z to fall in our color

space (Richards et al., 2002; Fan et al., 2001).

A more worrisome source of contamination comes from L and T dwarfs. To investigate

this, we compared our color selection region to the colors of L and T dwarfs (Hawley

et al., 2002) and find that they also are contained in the color region, albeit with large

uncertainties, as shown in Figure 2.2. From current observational studies, we estimate

that there may be O(1000) early L dwarfs in the SDSS footprint within the magnitude

limits of SDSS (Burgasser et al., 2010). Since we expect more dwarfs than giants at

these faint magnitudes, it is likely that a greater number of dwarfs are scattered into the

selection area through large errors than the number of giants scattered out. Objects in our

selection box that are not IGS are, nevertheless, likely interesting astrophysical objects

yielding more distant L dwarfs than currently known. We discuss ways to differentiate

between IGS and contaminants in section 2.5.

From the DR7 Star Table, we identified all stars that satisfy our color criteria and are

positioned at |b| > 20 to exclude potential disk contamination (including disk L and T

dwarfs). To ensure that each candidate has a stellar point spread function, we confirmed

that the object type flag in all 5 bandpasses were stellar2. We then removed all objects

1Background red galaxies have colors roughly 0.35 < r − i < 0.45 and 0.15 < i − z < 0.3 at z=0.1(Blanton et al., 2003). These colors will become redder with increasing redshift. For example, thebrightest and reddest galaxies in SDSS, LRGs at z=0.5, have r− i = 0.7 and i− z = 0.4 (Blanton et al.,2003). Since these colors do not approach our color selection region and since we have ensured stellarpoint spread functions for our candidates, we do not consider background galaxies as a significant sourceof contamination.

2Although we restrict our color criteria to the r , i , and z bands, in order to be conservative, we stillrequire the objects to have stellar point spread functions in the u and g bands as well.

45

that would be nearer than 300 kpc and further than 2 Mpc in the redder bandpasses,

assuming an M giant average absolute magnitude in each bandpass (Mr = 0.8,Mi =

−1.5,Mz = −3.5) yielding the following magnitude cuts: 23.2 < r, 20.9 < i, 18.9 < z

— since the r band is effectively below the magnitude limits of SDSS, we searched for

null detections in this band as well. We also eliminated objects that triggered any of the

following flags: BADSKY, BLENDED, CHILD, COSMIC RAY, EDGE, MAYBE CR,

MAYBE EGHOST, MOVED, NODEBLEND, and PSF FLUX INTERP.

We cross-checked our candidates with the 2MASS J-H color cut of Majewski et al.

(2003) since dwarfs and giants have distinctive J-H colors: J − Ks > 0.85, J − H <

0.561(J −Ks) + 0.36, J −H > 0.561(J −Ks) + 0.22 (top panel of Figure 2.3). Although,

note that the Majewski et al. (2003) color cut selects sub-solar metallicity M giants with

[Fe/H]= −0.4 ± 1.1 dex (Chou et al., 2007). This will make the giants selected by the

Majewski et al. (2003) cut bluer than the solar-metallicity giants selected in our sample.

The middle panel of Figure 2.3 shows a clear separation of the synthetic spectral

standard giants and dwarfs from Pickles (1998) at a J-H color around 0.8 (Bessell &

Brett, 1988). In general, J, H, and Ks magnitudes for our IGS candidates (16.86, 15.78,

and 15.56, respectively, for an M7III according to Covey et al. (2007)) are too faint to

appear in the 2MASS catalog. Since appearing in 2MASS would indicate that the source

is too bright or too close to be an IGS M giant we removed any candidate that did appear

in the 2MASS catalog, and to verify that they are nearby dwarfs, we plotted their J-H

colors shown in the bottom panel of Figure 2.3.

The completeness limits of J, H, and K filters in the UKIDSS (Lawrence et al., 2007)

survey are appropriate for our targets, however our search through the publicly-released

46

database (DR4) did not result in any matches to our candidates since we expect our

candidates lie in parts of the sky not yet covered by this release. Moreover, once the

UKIDDS survey is complete it will only cover about half of the area in the SDSS footprint.

After removing known dwarfs in 2MASS, we cross-referenced the IGS candidates with

the USNO-B catalog, an all-sky catalog that contains positions, proper motions, and mag-

nitudes in various optical passbands. Here, we removed those candidates with discernible

proper motions, ranging from 3 to 1412 mas/year, since the distances determined by the

proper motions indicate that they are likely objects closer than 353 pc. This eliminated

782 candidates.

2.3.1 Testing the color selection region with real data

Since our current technique for finding very late M giant IGS is based on idealized

solar metallicity spectra and synthetic colors, it is important to determine how robust

these colors are for known M7 III-M10 III stars. Unfortunately, there are no confirmed

very late M giant stars in the SDSS DR7 (or DR8) database with both spectra and colors.

While it is true that these stars are rare, the real difficulty is that spectral classification of

M giants is notoriously difficult, and the latest M giants can be spectral type variables, as

well. Since the SDSS database did not explicitly include the latest M giants, we decided

to take a three-pronged approach in checking M giant colors.

First, we searched through Simbad for spectroscopically-confirmed M7-M10 giants,

finding 53, 28, 4, and 0, respectively; many of these were listed in the Catalogue of Stellar

Spectral Classifications (Skiff, 2010). For each object, we cross-checked the spectral type

through all other publically-available catalogs on VizieR to determine if the star was a

47

known significant spectral variable, and if so, we discarded it. We then searched DR7 for

any star within 2 arcseconds of the target and obtained the photometry. Many of these

objects were nearby and saturated, and therefore appeared as several non-stellar sources

in the DR7 database – these were also discarded if the composite, corrected photometry

was not available. Only one of the remaining stars returned a result in the CAS and

appears as the blue star in Figure 2.4, which lies within our color cut.

Second, we acquired spectra of late-type giants observed as part of a study to quantify

the effects of gravity on the spectra of cool objects. These spectra were obtained with

the Low Resolution Imaging Spectrometer (LRIS, Oke et al., 1995) on the 10-m W. M.

Keck Observatory as part of a campaign to construct a systematic surface gravity “grid”

to further constrain spectral classifications of brown dwarfs (Kirkpatrick, in prep.). We

estimated the spectral type and log g parameters by eye and separated the latest M giant

subset for analysis, totaling 13 spectra. Examples of these spectra are shown in Figure

2.5. Using the SDSS transmission curves, we calculated the colors in the Sloan bands,

and as can be seen by the red stars in Figure 2.4, most of these stars do indeed lie in the

predicted color space.

Finally, as a further check of our M giant colors we used the Bruzual-Persson-Gunn-

Stryker (BPGS, hereafter; Laidler, V. et al, Synphot User’s Guide, Version 5.0 (Baltimore

STScI), 2005) stellar atlas of standard stars to obtain synthetic colors using the IRAF

Synphot task calcphot 3; the green points in Figure 2.4 represent these standard stars–

there were no available M9III-M10III standards in the atlas, which is expected because

3The i-z colors returned by calcphot for the M dwarfs are unreliable due to negative flux values in theBPGS stellar atlas.

48

these objects are all spectrum variables.

Figure 2.4 shows that the color cut we defined from synthetic SDSS colors is consistent

with the colors of known M giants from all three techniques.

If the reader is interested in seeing the colors of the stars we used from the BPGS

stellar atlas in the Johnson-Cousins filter set, a figure will be available online 4. The UBV

colors of these stars are consistent with the colors reported by Worthey & Lee (2006), as

well.

2.4 Results

We found a small region of color space, shown in Figure 2.2, in which the reddest

solar-metallicity M giants are isolated from the rest of the stellar locus. This region hosts

M7III-M10III stars, along with L dwarfs (Hawley et al., 2002).

Using our color selection criteria, we found 159,108 extinction-corrected objects in

SDSS DR7. After applying the distance cut and checking the data flags, we narrowed

the sample to 4181 objects. We then cross-correlated our sample with the 2MASS and

USNO-B surveys, removing any stars with dwarf-like J-H colors and any stars with non-

zero proper motions. Our final sample contains 677 IGS candidates. Table II.1 lists

positions, asinh magnitudes, r − i , and i − z colors for all 677 candidates. The right

panel of Figure 2.2 shows the location of the final set of IGS candidates with errors in

r − i/i− z color space.

4http://astro.phy.vanderbilt.edu/∼palladl2/

49

2.5 Discussion

As discussed in Section 2.1, IGS could be formed from several different methods.

Considering the Local Group’s current level of interactions, this population may likely be

comprised of high metallicity hypervelocity stars (HVS) ejected through the three body

mechanism. However, not enough is known about HVS and Local Group formation to

say this definitively, so probing the IGS sample may help us to constrain either or both

of these.

If every candidate were a solar metallicity IGS giant, they would be rare tracers of

a large underlying IGS population. Assuming a single burst of star formation 10 Gyrs

ago and a Salpeter initial mass function (IMF), these candidates represent O(10−4) of the

total number of IGS and O(10−3) of the total mass in IGS, and varies only slightly for

differing choices of IMF.

It is useful to compare this to theoretical predictions of stellar ejections from the Milky

Way (Kollmeier et al., 2009). Stars ejected from the galaxy center through three-body

interactions with a SMBH will typically have much higher metallicity than stars that

were stripped from satellite galaxies originating in the outskirts of a galaxy halo (e.g.,

Jacoby & Ciardullo, 1999a; Kirby et al., 2008). For example, if we assume that all of

the IGS are solar metallicity hypervelocity stars ejected by three-body interactions with

a binary black hole consisting of a SMBH and an intermediate mass black hole (IMBH),

then the total mass in stellar ejecta will be roughly equal to the mass of the IMBH (Yu &

Tremaine, 2003; Quinlan, 1996). Given the Milky Way SMBH mass of 4× 106M� (Ghez

et al., 2008), we would require an IMBH with mass roughly 105 M� as the companion,

50

independent of initial mass function. This IMBH mass is similar to the mass of the IMBH

proposed to be responsible for ejecting stars in the central region of the Galaxy (Lang

et al., 2011). This yields several IGS per square degree of sky and roughly tens of red

giant hypervelocity IGS in the SDSS footprint5.

Similar back of the envelope calculations suggest that there are O(1000) L dwarfs

located in the SDSS footprint, and realizing that late-type dwarfs are more common in

general, we anticipate that the majority of our IGS candidates are likely L dwarfs. If

these IGS candidates do turn out to be L dwarfs, then we have identified L-type dwarfs

at distances of 100-200 pc, which is up to 4 times farther than currently known (Schmidt

et al., 2010).

In an attempt to determine if the IGS sample has a distinct spatial distribution, we

conducted a set of 2-dimensional K-S tests that compared our candidates with template

samples drawn from 3 characteristic distributions: 1) an exponential disk with a scale

height of 300 pc to mimic an old stellar population, and a distance cut off of 200 parsec to

resemble an L dwarf distribution; 2) a random distribution; 3) and a set of observed hyper-

velocity stars (Brown et al., 2009). We convolved each template data set with the SDSS

footprint and employed the same galactic latitude cut as in our IGS sample. Assuming

that these are very cool dwarfs, the IGS sample should exhibit the same distribution on

the sky as the exponential disk, but the 2-d K-S test revealed otherwise: the probability

that these two samples come from the same underlying distribution is only 10−4. This

is ultimately not surprising since we removed any objects with a measurable proper mo-

tion, strongly selecting against L dwarfs within the disk. The second test with a random

5We expand on the expected number of total IGS and red giant IGS in Appendix A.

51

distribution resulted in an even smaller probability of 10−5, while the third test with the

hypervelocity sample yielded a somewhat higher probability of 10−2. Figure 2.6 shows

the position of our IGS candidates on the sky compared to the hypervelocity sample used

here.

2.6 Summary and Conclusions

We identified 677 intragroup stellar candidates from the SDSS DR7 using color cuts

based on solar metallicity spectral standards. These are extremely red stars with 1.3 <

i− z < 2.2, though the color would shift bluer with lower metallicity. As shown in Figure

2.2, the M giants in the region are not completely isolated. The latest M dwarfs and early

L dwarfs are possible sources of contamination.

Followup photometric observations of our candidates in the near to mid-infrared wave-

lengths may differentiate between late dwarfs and M giants. Future followup photometric

observations with a 4m class telescope may be promising, albeit impractical. For ex-

ample, the FLAMINGOS instrument on the NOAO 4m telescope could image all of our

candidates with a 113 hour total exposure time in each of the J and H bands, and over

600 hours of total exposure time in the K band for a 10-sigma detection, while this likely

would not be sufficient to distinguish M giants from dwarfs. Similarly, the J, H, and

K magnitude limits of NIRI on Gemini are appropriate for our targets, although would

require a prohibitively long total exposure time of 2031 hours to achieve a S/N of about

12.

Also, it is possible with long-term photometric followup observations on a 1m class

telescope to differentiate between dwarfs and giants based on variability, as late-type M

52

Table II.1. IGS candidates remaining after all criteria cuts [Complete version providedin Appendix C].

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

758882136836343139 60.5013 80.8760 24.4 1.3 24.7 0.6 24.3 0.7 22.0 0.2 20.3 0.2 2.3 1.7758882137910740030 62.9212 82.5298 25.2 1.2 25.0 0.6 23.2 0.4 21.0 0.1 19.6 0.1 2.2 1.4758882626993718584 63.3170 81.6950 26.5 0.6 24.8 0.6 25.3 0.7 22.0 0.2 20.3 0.2 3.3 1.6758877527803168329 94.6323 63.7038 25.1 0.9 24.1 0.3 24.5 0.5 21.2 0.1 19.8 0.1 3.3 1.4758877527266231607 94.8017 63.2633 24.6 0.7 24.4 0.5 24.5 0.6 21.8 0.1 20.4 0.1 2.7 1.4758877527266493955 95.9369 63.5501 25.2 0.7 24.8 0.6 25.6 0.5 22.7 0.3 20.7 0.2 2.9 2.0758878272976455144 105.3459 66.8553 25.3 0.9 24.4 0.4 24.1 0.4 21.8 0.1 20.2 0.1 2.3 1.6758878271902778853 105.8427 66.0785 23.8 0.7 24.7 0.4 24.6 0.5 22.3 0.2 20.8 0.2 2.3 1.5758884768580109918 107.9936 38.3022 24.8 1.1 25.1 0.7 24.4 0.6 21.9 0.1 20.4 0.2 2.6 1.4587738067260998978 109.5721 39.4395 25.3 0.9 25.7 0.6 24.6 0.7 22.1 0.2 20.0 0.1 2.5 2.1

giants tend to be highly variable.

Naturally, low resolution spectroscopic follow-up observations of these IGS candidates

would be ideal to confirm their luminosity class. The Calcium II Triplet (CaT) feature

at 8498A, 8542A, and 8662A is particularly useful for distinguishing late M dwarfs from

giants, being much more prominent in the spectra of late-type dwarfs (Reid & Hawley,

2005). In addition, the strength of the Calcium Hydride (CaH) feature between 6800A and

7000A is a good indicator of luminosity class (Cohen, 1978).

Once the confirmation is complete, we can test the efficiency of our color selection

technique, which will be useful for large data surveys like LSST. In fact, two surveys set

to launch in the coming year will be particularly well-tuned to find IGS M giants. The

DECam survey on the CTIO 4-meter telescope will observe over 1000 square degrees, with

magnitude limits of r=23.4, i=24.0, and z=22.9 – over two magnitudes deeper than SDSS

in z. An even deeper survey will launch on the Subaru telescope; the HyperSuprimeCam

plans to observe 2000 square degrees down to z=24.9 and y=23.7. Eventually, deeper

53

observations of IGS can reveal the metallicity of these stars – an important clue to their

original birthplace within the group or in situ in the intergalactic medium.

54

Figure 2.3: Top: Blue dots are SDSS Stripe 82 stars (Ivezic et al., 2007) that satisfy theMajewski et al. (2003) M giant color cuts. Larger red dots are M giants from Covey et al.(2007). The point located outside the color cut corresponds to an M10 spectral type. Alsonote that the late M giants (M7-M10) are located in the part of this color region that isleast populated, so they will be least likely to be identified by this cut. Middle: Red opencircles are M giants from Covey et al. (2007). Blue dots are M dwarfs from Covey et al.(2007). Bottom: IGS candidates with 2MASS JHK colors. The solid line represents theJ-H = 0.8 separation between dwarfs and giants.

55

Figure 2.4: Same as the left panel of Figure 2.2. The green stars overplotted here representM-giant standards, with spectral types between M6III and M8III, from the BPGS stellaratlas. The larger green dots are dwarfs with spectral types O through M, from the sameatlas. The photometry for these stars was obtained by implementing IRAF synphot tasks.The blue star represents the M giant identified from the Catalogue of Stellar SpectralClassifications (Skiff, 2010) with confirmed SDSS photometry. The red stars are the Mgiant contaminants in the Kirkpatrick (in prep.) data for which we received spectra.

56

Figure 2.5: Four of the spectra used to compare colors to our IGS candidates. Theresulting colors are shown in Figure 2.4.

57

Figure 2.6: The relative positions of our IGS candidates and the hypervelocity stars ofBrown et al. (2009) that were compared with the 2-d K-S test. The comparison was madebetween 522 IGS candidates, red dots, and 22 HVS, blue stars. Notice the higher densityof IGS candidates at the edges of the footprint signifying larger numbers of these stars atlower Galactic latitudes.

58

Chapter III

HYPERVELOCITY STAR CANDIDATES IN THE SEGUE G & K DWARF SAMPLE

Here we reprint, in its entirety, work published in the Astrophysical Journal, 2014,

Vol. 780, Article ID 7.

3.1 Abstract

We present 20 candidate hypervelocity stars from the Sloan Extension for Galactic

Understanding and Exploration (SEGUE) G and K dwarf samples. Previous searches

for hypervelocity stars have only focused on large radial velocities; in this study we also

use proper motions to select the candidates. We determine the hypervelocity likelihood

of each candidate via Monte Carlo simulations, considering the significant errors often

associated with high proper motion stars. We find that nearly half of the candidates

exceed their escape velocities with at least 98% probability. Every candidate also has

less than a 25% chance of being a high velocity fluke within the SEGUE sample. Based

on orbits calculated using the observed 6-d positions and velocities, few, if any, of these

candidates originate from the Galactic center. If these candidates are truly hypervelocity

stars, they were not ejected by interactions with the Milky Way’s supermassive black

hole. This calls for a more serious examination of alternative hypervelocity star ejection

scenarios.

59

3.2 Introduction

Hypervelocity stars (HVSs) are believed to be ejected by three-body interactions

with the supermassive black hole (SMBH) at the Galactic center (e.g., Hills, 1988; Yu

& Tremaine, 2003; Brown et al., 2005). During this process, energy and angular momen-

tum are transferred from the black hole to one of the stars in a binary system. The second

star loses energy and becomes bound to the black hole while the first is ejected from the

Galaxy. In this scenario HVSs can probe conditions in the Galactic center such as the

binary fraction, and even place limits on the existence of a second, tightly bound SMBH.

Semianalytical models predict that there may be approximately 100 HVSs within 8 kpc

of the Galactic center due to the break up of equal-mass binaries (Gould & Quillen, 2003;

Yu & Tremaine, 2003).

While the SMBH at the Galactic center remains the most promising culprit in generat-

ing HVSs, other hypervelocity ejection scenarios are possible, such as a close encounter of

a single star with a binary black hole (Yu & Tremaine, 2003). In this case, the star gains

energy from the binary black hole and is flung out of the Galaxy while the orbit of the

black hole binary shrinks (e.g., Quinlan, 1996; Sesana et al., 2006). Another alternative

hypervelocity ejection model involves the disruption of a stellar binary in the Galactic

disk; here a supernova explosion in the more massive component can accelerate the com-

panion to hypervelocities (e.g., Blaauw, 1961; Leonard & Dewey, 1993; Napiwotzki &

Silva, 2012).

At least 18 HVSs have been discovered in the Milky Way within the past decade with

velocities as high as 700 km s−1 (e.g., Brown et al., 2005; Edelmann et al., 2005; Hirsch

60

et al., 2005; Brown et al., 2009, 2012). So far, all confirmed HVSs are massive B-type stars

such as those observed around the central SMBH (e.g., Brown et al., 2009, 2012). However,

since the ejection mechanisms described above apply to any stellar mass, it is important

to search for HVSs among the larger set of longer-lived, lower mass stars (e.g., Quinlan,

1996). If a SMBH ejection mechanism is at play, then metal-rich stars originating from the

Galactic center ought to pollute the metal-poor halo. Previous attempts to mine Sloan

Extension for Galactic Understanding and Exploration (SEGUE) and SEGUE-2 stellar

halo data found no metal-rich, old ejected stars (Kollmeier et al., 2009, 2010). The lack of

a significant population of old, metal-rich HVSs suggests that the initial mass function at

the Galactic center is mildly top-heavy. Alternatively, hypervelocity ejection mechanisms

may be more complex than previously thought.

In this paper we identify the first set of G- and K-type candidate HVSs from SEGUE.

We discuss candidate selection in Section 3.2, including a description of the G and K

dwarf sample, and we address the significant proper-motion errors in Section 3.3. Section

3.4 contains orbital parameters for the HVS candidates, and Section 3.5 discusses possible

alternative origin scenarios. Finally, we summarize and conclude in Section 3.6.

3.3 Identifying HVS Candidates

Our candidates are drawn from the G and K dwarf stars in SEGUE (Yanny et al., 2009)

from the Sloan Digital Sky Survey (SDSS) Data Release 9 (DR9; SDSS-III Collaboration

et al., 2012). As part of SDSS (York et al., 2000b), SEGUE provides medium-resolution

(R ≈ 1800) spectroscopy over a broad spectral range (3800–9200 A). Probing more than

150 lines of sight, SEGUE covers ≈3500 deg2 of the sky, with spectroscopy of ≈240,000

61

Figure 3.1: Transverse versus radial velocities of our HVS candidates, in kilometers per second. Redlines indicate a transverse velocity

√2 times higher than the radial velocity, as expected for an isotropic

stellar distribution. Blue lines represent a transverse velocity 5 times higher than the radial velocity.The majority of our candidates show large transverse-to-radial velocity ratios, characteristic of a samplestrongly affected by large proper-motion errors. We caution that some of our HVS candidates may behigh-velocity flukes, and we calculate the likelihood of this in Section 3.3.2.

62

stars over a range of spectral types. Technical information about SDSS has been published

on the survey design (York et al., 2000b; Eisenstein et al., 2011), telescope and camera

(Gunn et al., 1998, 2006), and spectrographs (Smee et al., 2013), as well as the photometric

system (Fukugita et al., 1996b) and astrometric (Pier et al., 2003) and photometric (Ivezic

et al., 2004) accuracy.

G and K dwarfs are selected from the SDSS photometric data using simple color and

magnitude selection criteria. The 42,901 SEGUE G dwarfs are defined as having 14.0

< r0 < 20.2 and 0.48 < (g− r)0 < 0.55, while the 28,332 K dwarfs have 14.5 < r0 < 19.0

with 0.55 < (g − r)0 < 0.75 (Yanny et al., 2009). The subscript zero indicates that the

color and magnitude have been corrected for dust extinction, using estimates derived from

Schlegel et al. (1998). Each spectrum is analyzed with the DR9 SEGUE Stellar Parameter

Pipeline (SSPP), which provides estimates of effective temperature, surface gravity (log g),

[Fe/H], and [α/Fe] (Lee et al., 2008a,b; Allende Prieto et al., 2008; Smolinski et al., 2011;

Lee et al., 2011). We follow the quality protocol of Schlesinger et al. (2012) to remove

targets with poor signal-to-noise ratio (S/N <10), incalculable atmospheric parameters,

excessive reddening (greater than 0.5 mag in r), saturated photometry (r0 < 15), or flags

indicating temperature or noise issues. We also use the SSPP log g estimates to ensure

the stars are dwarfs, using a cut on log g as a function of [Fe/H] to isolate dwarf stars (K.

J. Schlesinger et al. 2014, in preparation).

For each star that satisfies these criteria, we determine its distance using the isochrone-

matching technique described by Schlesinger et al. (2012). Briefly, each star is matched

in [Fe/H] and (g− r)0 to 10 Gyr isochrones from the empirically corrected Yale Rotating

Stellar Evolution Code set (An et al., 2009). There are systematic distance uncertainties

63

introduced by using 10 Gyr isochrones, as well as the possibility of undetected bina-

rity; this leads to a systematic shift in distance of −3% for the most metal-rich stars,

while metal-poor stars are largely unaffected; this is factored into our distance estimates.

There are also random distance errors from uncertainties in photometry, [Fe/H], [α/Fe],

and, finally, isochrone choice. The total random distance uncertainty is dominated by

uncertainties in [Fe/H] and ranges from around 18% for stars with [Fe/H] > −0.5% to

8% for more metal-poor stars.

To identify HVSs, we convert the radial and tangential velocities to Galactic Cartesian

coordinates, as described below in Section 3.4.1, and choose a simple but conservative

initial total velocity threshold of 600 km s−1 to identify stars that exceed the Galaxy’s

escape velocity (e.g.; Smith et al., 2007). We then verify that each candidate exceeds

the escape velocity at its current location within the Galaxy. This procedure yields 42

preliminary HVS candidates of varying quality, which we further glean as described in

Section 3.3.1 below.

3.4 Estimating the Fidelity of Our Candidates

3.4.1 Proper-Motion Quality Cuts

The proper-motion distribution in SDSS is skewed toward large proper-motion errors.

We must ensure that the extreme velocities of our candidates are real rather than the

product of large errors. We describe our technique to ensure the robustness of our candi-

dates in this section. The first step in defining a clean hypervelocity sample is to assess the

quality of the proper-motion measurement. To determine the proper motions for SDSS

64

targets, Munn et al. (2004, 2008) matched each SDSS point source to the USNO-B cata-

log. The resulting SDSS+USNO-B catalog is 90% complete to g <19.7 and has statistical

errors of approximately 3−3.5 mas yr−1 and systematic errors of ≈0.1 mas yr−1 for each

component.

Munn et al. (2004) defined a number of criteria to ensure that the SDSS+USNO-B

proper motions are reliable; these conditions resulted in a version of the USNO-B catalog

with a contamination of less than 0.5%. The criteria were later revised by Kilic et al.

(2006) and are as follows1:

• The number of objects in USNO-B within a 1” radius of the SDSS target should be

1 (match=1).

• The rms residual for the proper-motion fit in right ascension and declination must

be less than 525 mas (sigRA < 525 and sigDEC < 525).

• There must be at least six detections (including the SDSS observations) used to

determine the proper motion (nFit = 6).

• The distance to the nearest neighbor with g < 22 must be greater than 7” (dist22

> 7).

Only three of our 42 preliminary candidates met all of the proper-motion quality

criteria, and we categorize these as “Clean.” We performed an in-depth analysis for the

remaining 39 stars, assigning each a likelihood of proper-motion contamination based on

the same criteria adopted by Kilic et al. (2006) for their white dwarf sample. They found

1The parameters listed in parentheses are available in the DR9 proper motions catalog in the SDSSCatalog Archive Server (CAS).

65

that the chance of contamination for a target with

• Six detections and a neighbor within 7” is less than1.5%;

• Five detections and no near neighbors is 1.5%;

• Five detections and a neighbor within 7” is 35%;

• Four detections and no neighbor within 7” is 51%; and

• Three detections and no neighbor within 7” is 89%.

We further checked for any potential blending issues by visually inspecting each candidate.

We categorize 17 stars as having “Reliable” proper motions, with 1.5% or less chance

of contamination and no visual blending. We categorize 10 stars as “Possible,” meaning

they have between 35% and 51% chance of contamination. Twelve stars were removed

because of visual blending.

We choose to consider only those candidates with “Clean” and “Reliable” designations.

Thus, our final sample contains 20 HVS candidates, all with greater than 98.5% probability

of robust proper-motion estimates.

We do expect that this final sample contains false-positive HVS detections. One way

to illustrate this is with Figure 3.1, which compares the transverse and radial velocities

of our HVS sample. For a random isotropic stellar distribution, the transverse velocity

should be roughly√

2 times higher than the radial velocity, and the fact that this sample

is predominantly composed of stars with much larger transverse-to-radial velocity ratios

is a classic signature of contamination by large proper-motion errors. While this does not

prove that all of the candidates are spurious, it does indicate that many of them may

66

be. Of course, a true hypervelocity sample would not be well represented by a random,

isotropic distribution, but we caution that it is premature to say that we have identified 20

HVSs. We conducted further statistical tests, described below, to evaluate the likelihood

that each HVS candidate is real.

3.4.2 Monte Carlo Sampling

Although the typical error in proper motion in the SEGUE database is ∼ 10 mas

yr−1, proper-motion errors can, for some stars, be much larger than expected for a normal

distribution, especially at the high-velocity end (Gould, 2003; Gould & Salim, 2003; Gould

& Kollmeier, 2004; Munn et al., 2004, 2008; Bond et al., 2010). With this in mind, we

consider the possibility that these HVS candidates may have true velocities much lower

than can be explained by the reported errors and that they are in fact bound to the

Galaxy.

In order to determine the true range of velocities for our HVS candidates, as well

as the probability that these candidates are bound given a more realistic error distribu-

tion, we built a Monte Carlo simulation to sample possible orbital parameters for each

HVS candidate. Dong et al. (2011) obtained a proper-motion error distribution for the

SDSS+USNO-B catalog by compiling proper motions for a sample of SDSS quasars that

met the Kilic et al. (2006) criteria. We randomly resampled a million realizations of each

HVS candidate’s kinematics from the Dong et al. (2011) non-Gaussian proper-motion er-

ror distribution and Gaussian radial velocity errors. We also resampled each candidate’s

position, assuming Gaussian errors in the distance determinations as well. We find that

13 of the 20 candidates remain hypervelocity with greater than 90% probability.

67

Figure 3.2 shows the distribution of velocities drawn randomly from the errors for the

three least and most bound candidates. In most cases, the drawn velocity well exceeds

the escape velocity, represented by the vertical dashed lines.

We performed a second Monte Carlo test to quantify the chance that these high

velocities are simply the extreme tail end of the velocity error distribution within the

entire SEGUE G and K dwarf sample. Here we construct a new mega-SEGUE sample

built from 1000 realizations of each SEGUE star, in which each realization is drawn from

the error distribution in proper motion, radial velocity, and distance as described above.

We then calculate the “interloper likelihood” for each candidate with respect to the mega-

SEGUE sample; this is the probability that a slow, noncandidate star within our sample

could have had the observed velocity of a particular candidate, given the errors:

P (interloper, i) = 1− nHVS(v ≥ vcand,i)

ntot(v ≥ vcand,i), (3.1)

where nHV S(v ≥ vcand,i) is the number of stars in the mega-SEGUE sample with velocity

greater than or equal to the observed velocity of candidate i that were originally tagged

as hypervelocity in the data and ntot(v ≥ vcand,i) is the total number of stars in the

Monte Carlo sample with velocity greater than or equal to the candidate’s velocity. All

candidates have less than a 25% “interloper likelihood,” and more than half have less

than 10%. Together, these two tests indicate that some of our candidates may in fact be

the result of a statistical fluke. However, we expect the bulk of the candidates to remain

hypervelocity.

Table III.1 lists the velocity of each candidate determined from the proper motions

68

reported in DR9, the minimum velocity calculated from a million realizations of the proper

motion, radial velocity, and distance errors, the escape velocity for each candidate in a

spherically symmetric Galaxy, the probability that the candidate may be bound given the

escape velocity at its position, and the interloper likelihood as described above.

3.5 Orbits of HVS Candidates

3.5.1 Galaxy Model

We construct an analytical, multicomponent model of the Milky Way gravitational

potential to predict the orbits of stars in the Galaxy based on the initial six-dimensional

observed position and velocity. The model is easily modifiable and can be tuned to reflect

the observed Galactic structural parameters.

Our model includes the following components: a central SMBH with MSMBH = 4 ×

106M�; a spherical Hernquist bulge (Hernquist, 1990) with Mbul = 4.5 × 109M� and

rbul = 2.5 kpc; Miyamoto−Nagai thin and thick disks (Miyamoto & Nagai, 1975) with

Mthin = 6× 1010M�,Mthick = 6× 109M�, 0.3 kpc thin-disk scale height, 1 kpc thick-disk

scale height, and 3 kpc scale lengths for both; and a Navarro−Frenk−White (NFW) dark

matter halo (Navarro et al., 1997) following the formalism of Lokas & Mamon (2001); we

chose MNFW = 1012M�, Rvir = 200 kpc, and c = 10 for the Milky Way. Recent studies

have argued for a shorter thick-disk scale length (e.g.; Cheng et al., 2012; Bovy et al.,

2012b; Bensby et al., 2011); however, this change would have a negligible effect on our

results because of the comparatively low mass of the thick disk component.

The model can also be tuned for varying degrees of axisymmetry or triaxiality in the

69

halo. For this study we use both spherical and triaxial models. For the triaxial model,

we adopt the axis ratios b/a = 0.99 and c/a = 0.72 (Law & Majewski, 2010).

The Galactic Cartesian coordinate system used here is centered on the Galactic center;

the x-axis points from the center toward the Sun (located at x = 8.2 kpc (Schonrich,

2012)), the y-axis points along the direction of Galactic rotation, and the z-axis points

toward the North Galactic Pole. To calculate velocity in this coordinate system, we

convert radial velocity, distance, and proper motions to U , V , and W in the Galactic

coordinate system. Note that issues with astrometry in DR8, as explained in Section

3.3.5 of Aihara et al. (2011b) and the associated erratum (Aihara et al., 2011a), have

been resolved for the DR9 astrometry used here. We choose the velocity of the local

standard of rest to be 238 km s−1, and the motion of the Sun with respect to that is

U = −13.8 km s−1, V = 12.24 km s−1, and W = 7.25 km s−1 (Schonrich, 2012; Schonrich

et al., 2010). This Galactic model is consistent with the measured proper motion of SgrA*,

6.379± 0.026 mas yr−1 (Reid & Brunthaler, 2004). Then, U , V , and W are transformed

into the Galactic Cartesian coordinate system, and we calculate the orbits backward in

time for 1 Gyr using a fourth-order Runge−Kutta integrator. The choice of 1 Gyr is

sufficient to discern the direction of origin while not being significantly influenced by a

changing Galactic potential.

We examine the variation of each candidate’s orbit given the errors described in Section

3.3.2. Figure 3.3 shows the 1σ and 2σ orbits for HVS 20, indicating that for some of the

candidates the velocity errors are sufficiently large that the candidate itself may be bound.

We find that the differences between orbits in the spherical versus the triaxial model are

negligible for unbound orbits, since the stars have little time to respond to the halo

70

potential. Therefore, for simplicity, when discussing unbound orbits we show only those

in the spherical case. However, in instances when the orbit may be bound, as for HVS 20

in Figure 3.3, the halo shape definitely influences the candidate’s trajectory, suggesting

that marginally bound stars may help constrain halo triaxiality.

3.5.2 Origins

As shown in Figure 3.4, the trajectories of these HVS candidates do not originate

from the Galactic center, which would be expected if the stars were ejected by three-body

interactions with the SMBH. Instead, they appear to be coming from all directions, which

suggests that other ejection processes may be at play.

We considered the SMBH at the center of M31 as a possible source (Sherwin et al.,

2008), and given the velocities of the stars, we find the required flight time to reach

the solar neighborhood would be approximately 1 Gyr. Figure 3.4 shows the orbits cor-

responding to the seven most unbound candidates, each with a 1σ “wedge” of possible

orbits. It can be seen that the candidates could not have come from M31’s SMBH position

1 Gyr ago (dashed lines). The orbits of the other 13 candidates are consistent with not

arriving from M31. Therefore, the SMBH at the center of M31 is not responsible for eject-

ing these stars. However, this does not exclude other Galactic and extragalactic sources

such as globular clusters, satellite galaxies, or the centers of distant galaxies within ∼ 10

Mpc.

71

3.6 Discussion

3.6.1 Chemical Tracing

Since it is more difficult to trace the past orbits of globular clusters and known satellite

galaxies because of tidal stripping, shocks, and other mass-loss effects, we cannot say with

certainty whether these stars could have originated in the Galactic disk, the bulge, or

globular clusters. Another approach to determine whether these candidates belong to a

particular population is to examine their chemical compositions.

We compared the metallicities of our candidates with the metallicity distribution func-

tions (MDFs) of known globular clusters (Harris, 1997), the SEGUE G and K dwarf

samples representative of the Milky Way disk population (Schlesinger et al., 2012), the

Galactic bulge (Sadler et al., 1996), and by extension the bulge of M31, assuming a peak

metallicity of +0.23 (Jacoby & Ciardullo, 1999b). We also compared the metallicity dis-

tribution of our candidates with the MDF of the Galactic halo, although with a peak at

[Fe/H] < −1 (An et al., 2013) it is clearly inconsistent with our candidates.

The MDFs for each population are shown in Figure 3.5. As perhaps expected, the

metallicity of the HVS candidates is consistent with the G and K dwarf samples in the

disk. Their metallicities are also largely consistent with the high-metallicity end of the

globular cluster population and the low-metallicity end of the Galactic (and M31) bulge.

Similarly, the stars’ [α/Fe]-values are broadly consistent with these stellar populations.

Unfortunately, based on the information here, none of these populations can be decisively

ruled out as a possible source, although it is clear that these HVSs do not originate from

the metal-poor globular cluster system.

72

Figure 3.2: Velocity distribution for a million random samples of the velocity error distribution for thethree least and most bound HVS candidates. Dashed lines show escape velocity of each candidate.

Figure 3.3: Orbit of HVS 20, a candidate with a “Reliable” proper-motion measurement but the largestprobability of being bound, shown by the black lines. Also shown are the resulting orbits for the samecandidate with 1σ (red lines) and 2σ (blue lines) velocity errors from the million Monte Carlo realizations.Left, two-dimensional projections in the spherical dark matter halo; right, the same for the triaxial model.The black dots and plus signs represent the locations of the Galactic center and the Sun, respectively,while the pale blue ellipses provide a rough scale for the extent of the disk. The five-pointed star in eachpanel marks the current position of HVS 20. The top row is a top-down view of the Galaxy while themiddle and bottom rows are side views along the disk. Here we show that some candidates may in factlive on very bound orbits, and in such cases the shape of the orbit is strongly influenced by the triaxialityof the halo.

73

Figure 3.4: Orbits of the seven HVS candidates that are unbound with at least 98% proability, overthe past 1 Gyr. As in Figure 3.3, the black dots and plus signs represent the locations of the Galacticcenter and the Sun, respectively, while the pale blue ellipses provide a rough scale for the extent of thedisk. The shaded regions flanking the orbits of the same color represent the “wedges” of possible orbitsgiven the 1σ velocity errors for the corresponding candidate. The like-colored stars mark the currentpositions of the candidates. None of the orbits plotted here intersect near the Galactic center, suggestinga different origin for these stars. In additional, if these stars had been traveling for 13 Gyr, they may haveoriginated from as far as tens of megaparsecs away. The dashed lines, highlighted in yellow for visibility,point toward M31’s location 1 Gyr ago, assuming M31 proper motion, radial velocity, and distance fromSohn et al. (2012). This interval was chosen to roughly coincide with the travel time of a hypervelocitystar originating in M31. None of these HVS candidates seem to be coming from M31, which therefore isruled out as a possible origin.

74

Tab

leII

I.1.

Ste

llar

and

kin

emat

icpar

amet

ers

for

the

20H

VS

candid

ates

.

d%

“In

terloper

HVS

IAU

Name

r 0[F

e/H]

[α/Fe]a

(kpc)

vrb

vtc

vd

vm

ine

vesc,S

phf

Bound

Likelihood”

Rating

1J060306.77+

825829.1

18.07

−0.06

0.10

3.70

−76.0

56.1

802.2

92.2

533.6

6.35

0.02

Clean

2J023433.42+

262327.5

19.01

−0.15

0.09

5.68

−25.6

15.7

628.6

290.0

517.3

7.43

0.18

Clean

3J160620.65+

042451.5

19.01

−0.91

0.40

4.06

31.7

23.7

641.8

195.1

588.9

34.88

0.15

Clean

4J113102.87+

665751.1

16.15

−0.83

0.46

1.04

−54.9

237.7

1296.7

587.4

552.3

0.0

0.00

Reliable

5J185018.09+

191236.1

18.16

−0.34

0.19

3.19

58.0

61.5

1086.8

378.9

576.5

0.04

0.00

Reliable

6J035429.27−

061354.1

18.07

−0.55

0.26

3.13

80.2

46.2

916.3

286.6

534.5

0.07

0.01

Reliable

7J064337.13+

291410.0

18.01

−0.55

0.35

3.06

20.4

38.1

793.9

285.0

530.2

0.30

0.02

Reliable

8J202446.41+

121813.4

17.74

−0.65

0.26

2.48

6.26

51.8

769.1

376.3

570.3

1.01

0.03

Reliable

9J011933.45+

384913.0

18.26

−0.67

0.22

3.31

−36.9

65.5

937.3

185.2

536.3

1.20

0.00

Reliable

10

J172630.60+

075544.0

18.46

−0.67

0.39

3.82

−2.2

59.7

992.9

233.5

591.0

1.34

0.00

Reliable

11

J073542.35+

164941.4

18.35

−0.23

0.12

3.70

78.2

28.8

712.9

285.4

527.3

2.89

0.07

Reliable

12

J025450.18+

333158.4

18.25

−0.70

0.16

3.14

−62.4

42.8

731.4

265.1

532.9

3.77

0.05

Reliable

13

J134427.80+

282502.7

18.32

−1.27

0.44

2.91

2.5

44.0

715.7

270.5

557.0

4.42

0.07

Reliable

14

J225912.13+

074356.5

18.76

−0.56

0.37

4.60

−97.8

44.9

840.7

121.8

550.0

5.86

0.01

Reliable

15

J095816.39+

005224.4

17.51

−0.80

0.28

2.22

1.6

59.2

649.8

248.7

546.5

15.98

0.14

Reliable

16

J074728.84+

185520.4

17.81

−0.24

0.13

3.26

43.9

58.1

672.8

55.3

530.7

19.70

0.11

Reliable

17

J064257.02+

371604.2

16.87

−0.33

0.21

1.78

6.2

49.1

601.4

305.4

540.9

20.01

0.24

Reliable

18

J165956.02+

392414.9

19.22

−1.14

0.48

4.35

−205.1

33.0

649.1

170.0

562.3

21.30

0.14

Reliable

19

J110815.19−

155210.3

19.01

−0.99

0.35

4.56

131.2

30.1

622.7

162.0

545.8

23.69

0.19

Reliable

20

J145132.12+

003258.0

19.47

−0.59

0.12

5.88

88.0

16.5

606.7

193.1

579.8

43.24

0.23

Reliable

aNote

there

are

larg

euncertaintiesin

these

measu

rements

atth

eS/N

ofth

ese

candid

ate

s.

bRadialvelocity,in

km

s−1,is

taken

stra

ightfrom

theSSPP

withoutany

corrections.

cTota

lpro

permotion,in

masyr−

1,is

calculate

dfrom

theµR

AandµD

ec

valu

eslisted

inth

eCAS

withoutany

corrections.

dThis

isth

eto

talvelocity

ofth

ecandid

ate

,in

km

s−1,after

conversion

toth

eGalactic

Cartesian

coord

inate

system

desc

ribed

in§4

.1,before

any

error

considera

tion.

eThevalu

ehere

isth

emin

imum

tota

lvelocity,in

km

s−1,dete

rmin

ed

from

amillion

realizationsofpro

permotion,ra

dialvelocity,and

dista

nceerrors

dra

wn

from

their

distrib

utionsdesc

ribed

inSection

3.3.

fTheesc

apevelocity,in

km

s−1,atth

estar’sposition

ina

sphericalpote

ntial.

75

3.6.2 Alternative Origins

As shown in Figure 3.4, none of the HVS candidates are coming from the Galactic

center or from the direction of M31. The popular ejection mechanisms described inSection

3.1 involve a central SMBH and cannot explain these stars. The question where these

stars originated, and how they gained such high velocities, remains.

One of the best-known hypervelocity mechanisms involves a binary system in the disk,

in which a supernova explosion ejects the companion star (e.g.; Blaauw, 1961). There are

many lesser known hypervelocity ejection mechanisms as well. For example, multibody

ejections from the dense central regions of globular clusters (e.g.; Poveda et al., 1967)

including globular clusters that may have dissipated over the lifetime of the Galaxy (e.g.;

Gnedin & Ostriker, 1997; Chernoff & Weinberg, 1990; McLaughlin & Fall, 2008) may boost

a star to hypervelocities. In addition, there could be a three-body interaction involving

an intermediate-mass black hole or otherwise very massive star (e.g.; Gvaramadze et al.,

2009). A final hypervelocity ejection mechanism involving a stellar dynamical process

could be the partial tidal disruption of a single star around a SMBH (Manukian et al.,

2013).

Furthermore, three-body interactions between galaxies, such as M31 (e.g.; Caldwell

et al., 2010) and the Large and Small Magellanic Clouds (e.g.; Chandar et al., 2010),

have been suggested as possible hypervelocity ejection mechanisms, although we have

already ruled out M31 specifically. HVSs may also receive an energy boost during the

tidal stripping process as long streams are stripped from an accreted satellite (e.g.; Abadi

et al., 2009; Caldwell et al., 2010; Piffl et al., 2011; Fouquet et al., 2012; King et al., 2012).

76

3.6.3 Follow-up Analysis

A significant fraction of the candidates failed the dist22 > 7 requirement, meaning

that photometric blending from a near neighbor may have affected the proper-motion

determination. A larger number of the candidates suffer from too few detections in the

SDSS+USNO-B catalog. Confirming these candidates as HVSs would require additional

astrometric analysis in order to verify their proper motions; the Hubble Space Telescope

Fine Guidance Sensor may be appropriate.

There is also the possibility that these candidates are unresolved spectroscopic binaries,

which could imprint a large radial velocity signal. Future, higher resolution spectroscopic

observations could easily decide this issue and would also allow a more detailed chemical

analysis to shed light on their origins.

3.6.4 Constraints on the Initial Mass Function

The fact that we find no low-mass HVSs coming from the Galactic center continues to

pose a problem for a universal initial mass function and an unbiased binary ejection mech-

anism. If we simply assume a Salpeter initial mass function and a mass-blind dynamical

process, we would naively expect roughly 150 HVSs in the 0.6−1.2 solar mass range in

our sample, compared with the 14 known 3−4 M� HVSs (Brown et al., 2009). Either the

initial mass function near the Galactic center is top-heavy or the process acting at the

Galactic center ejects over 10 times more high-mass stars than low-mass ones. There is

tentative evidence from the Arches and other young star clusters at the Galactic center

that the initial mass function is top-heavy, with a slope of about −1.6 (Figer et al., 1999),

77

although this is a matter of debate. If we adopt this slope for our initial mass function,

then we still should have observed roughly 40 HVSs with spectral types G and K, which

would require an ejection mechanism that favors massive stars by more than factor of 32.

Our constraints on the initial mass function are consistent with the findings of Kollmeier

et al. (2010), who searched for metal-rich F/G halo HVSs. This earlier study placed

stricter limits on the ejection mechanism, however, because F/G stars would be expected

to accumulate in the halo over their main-sequence lifetimes, while our sample probes

only stars passing through the solar neighborhood; stars ejected from the Galactic center

through stellar binary disruption, for example, would reach and pass through our sample

in mere tens of millions of years. Our results are also consistent with the constraints from

Zhang et al. (2013), who considered the S stars at the Galactic center to be the captured

companions of binary star tidal disruption, a process that ejects the second star.

2We expand on the determinations of the expected number of HVSs in Appendix D.

78

3.7 Summary and Conclusions

We report a set of 20 hypervelocity candidates from the SEGUE G and K dwarf sample.

These candidates have velocities greatly exceeding the escape velocity at their respective

positions in the Galaxy, albeit with large proper-motion errors. Monte Carlo estimates

of the position and kinematics of these stars show that seven of the 20 exceed the escape

velocity at their respective locations within the Galaxy with at least 98% probability and

that each candidate’s interloper likelihood is less than 25%.

Surprisingly, an orbit analysis indicates that none were ejected from the Galactic

center. The confirmation of these candidates as HVSs argues for a more careful exploration

of alternative ejection mechanisms such as interactions within globular clusters, dwarf

galaxies, or tidal tails, as well as ejections from supernovae in the Galactic disk.

If these stars are truly hypervelocity, their spectra could already contain clues to their

origin. For example, abundance patterns indicative of supernova contamination would

confirm or rule out a candidate’s having been ejected from a high-mass binary system

(Przybilla et al., 2008).

One remaining question is why these stars were not identified in previous HVS cam-

paigns. A possibility is that prior searches focused on extreme radial velocities (e.g.;

Brown et al., 2005). While the radial velocities of our candidates are relatively modest,

it is the addition of proper motions that boosts these stars into hypervelocity candidacy.

Naturally, our sample also explored a cooler spectral type than previous work. Future

surveys may be more successful in identifying HVSs with both radial velocity and proper-

motion measurements.

79

We are expanding our search for HVS candidates to the entirety of the SDSS DR9 sam-

ple in order to include all spectral types. Analysis of any additional candidates identified

in this search, as well as follow-up, is deferred to a future paper.

80

Figure 3.5: Normalized metallicity distribution functions of our candidates (shaded), compared withG dwarfs (red), K dwarfs (green), globular clusters (blue), and the Galactic bulge (cyan).

81

Chapter IV

WORK IN PROGRESS

4.1 A Global Search for G/K-type Hypervelocity Stars

4.1.1 Motivation

The G- & K-dwarf sample of Schlesinger et al. (2012), used in Palladino et al. (2014),

was carefully selected to be representative of the disk around the Solar neighborhood. This

sample, while statistically robust, introduces selection biases in a search for hypervelocity

stars. Even if a HVS is ejected through interactions within the disk, the timescales on

which HVSs traverse the Galaxy are such that we should not necessarily expect to find

them lingering in the Solar neighborhood.

A true HVS found within the disk may be explained by a very recent, nearby, disk

ejection (e.g.; Blaauw, 1961). Alternatively, the HVS could be ‘just passing through’ as

a hypervelocity interloper originating from another region of the Galaxy, likely the bulge

(e.g.; Hills, 1988; Brown et al., 2005, 2012). The area of the Solar neighborhood targeted

by the Schlesinger et al. (2012) sample is such that either scenario would not contribute

significantly to the total HVS population. Conversely, assuming an un-biased ejection

geometry, regardless of origination site, it is more likely that HVSs are quickly flung out

into the halo. So, while there are many advantages of using the G- and K-dwarf sample of

Schlesinger et al. (2012), this section is dedicated to performing a global search for G/K-

type HVSs within the SEGUE database by loosening the selection criteria to include stars

outside the disk as well.

82

4.1.2 Candidate Selection

The global search for G/K-type hypervelocity stars was performed with a query of

the twelfth and final data release of SDSS-III by selecting stars with extinction corrected

(g−r)0 colors and r0 magnitudes indicative of G and K-type stars, as described in Section

3.3. The query returned 120,679 G-type stars and 173,790 K-type stars.

Subsequently, we remove any star for which effective temperature, surface gravity,

spectral type, metallicity, or radial velocity were not determined (ie. values of -9999

or “unknown”). This cut results in 130,990 targets. We follow the additional quality

assurances of Schlesinger et al. (2012) which also considered poor signal-to-noise, excessive

reddening, saturation, and flags assigned by the SSPP. We do not, however, consider the

magnitude limit and distance cuts of Schlesinger et al. (2012). Then, we apply the proper

motion quality criteria of Kilic et al. (2006) and retain only those stars that satisfy the

“clean” designation, described in section 3.4.1. This step results in a sample of 103,238

G/K-type stars.

An estimation of the distance to each star was determined by employing the distance

modulus with average absolute magnitudes assigned by the following equation (Ivezic

et al., 2008):

Mr = −2.85 + 6.29(g − i)− 2.30(g − i)2 + ∆Mr, (4.1)

where

∆Mr = 4.50− 1.11[Fe/H]− 0.18[Fe/H]2. (4.2)

Absolute magnitudes determined from this method are accurate to within 0.1 magnitude

83

only for stars with 0.3 < (g− i) ≤ 1.0 (Ivezic et al., 2008). Finally, dwarfs were separated

from giants with a simple log(g) cut at 3.5; dwarfs with log(g) > 3.5 and giants with

log(g) < 3.5. There are 85,268 G- and K-dwarfs (17,970 giants).

To identify hypervelocity star candidates, we convert the radial and tangential veloci-

ties to Galactic Cartesian coordinates and choose the same initial total velocity threshold

of 600 km/s as in Section 3.3, and a maximum velocity cut of 10,000 km/s. Again, as in

Palladino et al. (2014), we require that each candidate exceed the escape velocity at its

current location within the Galaxy. This procedure yields 28 HVS candidates.

4.1.3 Preliminary Results

As an initial comparison of the results of the global search to the sample of Schlesinger

et al. (2012), we compare the positions of the samples on the sky in Figure 4.1. We note

that both samples cover the SDSS footprint. The differences in the bottom panels of

Figure 4.1 are due to the distance cuts placed by Schlesinger et al. (2012) to isolate a

population of disk stars.

The HVS candidates presented in Palladino et al. (2014) have transverse velocities

significantly greater than their radial velocities (cyan 5-pointed stars in Figure 4.2), an

indication of a sample contaminated by large proper motion errors. We perform the same

comparison of transverse and radial velocities for the HVS candidates identified from the

global search for G/K-type stars (magenta 5-pointed stars in Figure 4.2). We find that

this sample is not biased in velocity– if anything, there are more candidates with velocities

dominated by the radial component, which is a reasonable expectation for a population

of HVSs zipping out of the Galaxy.

84

Finally, at this stage of the investigation we look at the distributions of total velocity,

Figure 4.3, and metallicity, Figure 4.4. We find the majority of the global-search HVS

candidates have comparable velocities to the HVS candidates published in Palladino et al.

(2014).

We also note that the metallicity distribution is bimodal (potentially trimodal) and

does not strongly resemble any of the comparison populations– published HVS candidates,

disk G/K-dwarfs, globular clusters, and bulge stars. The high-metallicity peak at [Fe/H]>

−0.5 is especially interesting. Perhaps we are seeing a composite population of artificially

velocity-boosted halo field stars and ejected bulge stars.

4.1.4 Discussion

The results presented in the previous section are preliminary and require further con-

sideration. One critical question that needs to be addressed before publication is: If the

Schlesinger et al. (2012) sample of G/K-dwarfs is only a subset of the global search for

G/K-type stars, why did we not recover the HVS candidates of Palladino et al. (2014)?

Other, marginally less perplexing, questions include: Why did we need to enforce a

maximum velocity cut of 10,000 km/s? and: Are the distances determined by equation 4.1

compared to the distances determined by Schlesinger et al. (2012), especially considering

that we did not restrain the g − i color of the sample to the range deemed valid for

equation 4.1 (Ivezic et al., 2008)?

Once the initial candidate selection is refined, we can start to answer the more in-

teresting science questions. To establish the probability that the candidates are HVSs

requires errors on the distance determinations, which at present, we do not have (but can

85

obtain by convolving the errors on the stellar parameters). Orbits for each candidate will

need to be calculated to determine their place of origin, and whether a SMBH ejection

can explain any or all of the new candidates. Furthermore, as an initial pass, we segre-

gated the giants out for a fair dwarf-to-dwarf comparison. However, we ultimately want

to consider the giants in the global sample as well and what they might contribute to the

unbound stellar population in the Milky Way.

4.2 F-type Hypervelocity Star Candidates

4.2.1 Motivation

Since there are 18 confirmed O/B-type HVS, consistent with SMBH ejection (Brown

et al., 2012) we know that the Hills mechanism operates at the center of the Galaxy.

If we add that Palladino et al. (2014) found zero low-mass HVS candidates originating

from the Galactic Center, we have compelling evidence that the ejection mechanism may

preferentially boost only the most massive stars to hypervelocities and/or that the initial

mass function at the Galactic center is extremely top-heavy. Now, we search for HVS can-

didates within a sample of SDSS F-type stars as an attempt to populate the intermediate

mass range to constrain the mass-dependence of the ejection mechanism.

The sample we use for this search is adapted from the sample of Allende Prieto et al.

(2014), originally selected to study abundances in the Sloan survey. I combine the dis-

tances determined by Fernandez-Alvar et al. (in prep) with proper motions, radial veloc-

ities, and stellar parameters from the SDSS Catalog Archive Server (CAS). The sample

contains 12,673 F-type stars.

86

4.2.2 Candidate Selection

From the initial sample of 12,673 F-type stars, we perform a similar cleaning procedure

as described in the sections above. First, we remove stars with undetermined effective

temperature, metallicity, or surface gravity. Then, we apply the proper motion quality cri-

teria of Kilic et al. (2006) and retain only those stars that satisfy the “clean” designation,

described in section 3.4.1. This step results in a sample of 11,779 F-type stars.

Similarly, we separate dwarfs from giants with a cut on surface gravity at 3.5. This

cut returns 10,590 F-dwarfs and 1,189 F-giants. For this sample, we rely on the distances

determined by Fernandez-Alvar et al. (in prep).

F-dwarf hypervelocity star candidates are identified via the same procedure outlined

in section 4.1.2. We find 98 preliminary HVS candidates with v > 600 km/s and 95 candi-

dates with v > Vesc. With both distance and distance errors provided by Fernandez-Alvar

et al. (in prep) we are able to initiate the statistical analysis stages of the investigation.

Via Monte Carlo simulations, described in detail in section 3.4.2, we find that 34 of the

preliminary F-dwarf HVS candidates are unbound at least 90 % of the time and 8 are

unbound at least 95% of the time.

4.2.3 Preliminary Results

We identified 95 F-dwarf HVS candidates with total velocities exceeding the escape

velocity at their respective locations. We performed the first statistical test to determine

each candidate’s probability of being bound to the Galaxy, described in Palladino et al.

(2014) and section 3.4.2. We identified 34 F-dwarf HVS candidates that are unbound with

87

at least 90% probability and 8 F-dwarf HVS candidates with at least 95% probability.

Figure 4.5 shows the velocity distribution of the 8 highly unbound candidates compared

to the sample of 95 F-dwarf candidates. The F sample yields an overall similar distribution

to that of the global G- and K-dwarf sample in section 4.1– the majority of the candidates

with vtot < 2000 km/s and a tail extending to much higher velocities at ∼ 6000 km/s.

Figure 4.6 shows the metallicity distribution of the 95 F-dwarf HVS candidates and

the 8 candidates that comprise the highly unbound subgroup. The F-dwarf HVS candi-

dates are much more metal poor than even the F sample from which they were selected.

However, the 8 highly unbound candidates, with a peak at [Fe/H] ∼ −1.7, roughly align

with the metal-poor peaks of both the F sample and globular cluster distributions.

4.2.4 Discussion

The results presented in the previous section are preliminary and require further con-

sideration. We are currently awaiting updated distance determinations for the F-star

sample. Once in hand, we will be able to fully characterize any HVS candidates within

the sample as was done in Palladino et al. (2014), including orbits and all statistical tests.

We would also like to compare the distances determined by the methods of Allende Prieto

et al. (2006, 2014) and Fernandez-Alvar et al. (in prep) to the distances determined by

equation 4.1.

Again, we plan to ultimately consider F-giants as well, but for reasons outlined in

Section 4.1.2 we postpone their analysis to a later date.

88

Figure 4.1: Top: Equatorial, RA and Dec, positions of the G/K-type stars returned by the globalsearch (black) and the G/K-dwarfs of Schlesinger et al. (2012) (red). Both samples probe all areas of theSDSS footprint. Bottom left: Cartesian, R and z, positions of the two samples. Bottom right: Same asbottom left, zoomed in to see the extent of the Schlesinger et al. (2012) sample. The differences in thebottom two panels are due to the distance cuts applied by Schlesinger et al. (2012).

89

Figure 4.2: The transverse velocity, vt, compared to the radial velocity, vr, for the HVS candidates ofPalladino et al. (2014) (cyan stars) and the global-search HVS candidates (magenta stars). The red linesindicate vt

√2 times larger than vr, expected for an isotropic stellar population. The blue lines represent

vt 5 times larger than vr, indicative of a sample dominated by the transverse velocity. The vast majorityof the cyan points fall between the blue lines, suggesting that those candidates may suffer from largeproper motion errors. Conversely, the magenta points are generally distributed throughout, suggestive ofan unbiased sample. Upon close inspection, roughly half of the global-search HVS candidates fall belowthe red lines– a strong indication that they follow radial orbits, not unexpected for HVSs.

90

Figure 4.3: The velocity distribution of the global-search HVS candidates. All of the Palladino et al.(2014) HVS candidates fall within the first bin, with v < 1500 km/s. The majority of the HVS candidatesrepresented here have similar velocities to the published candidates.

91

Figure 4.4: The metallicity distribution of the global-search HVS candidates (magenta) and the pub-lished HVS candidates (grey) compared to disk G/K-dwarfs (top), globular clusters (middle), and bulgestars (bottom). While the published HVS largely follow the distribution of the disk sample, the global-search candidates do not closely resemble any of the populations shown here.

92

Figure 4.5: The velocity distribution of the 95 F-dwarf HVS candidates (blue) and the 8 candidateswith at least 95% probability of being unbound.

93

Figure 4.6: The metallicity distribution of the 95 F-dwarf HVS candidates (grey) and the 8 candidatesthat are unbound with at least 95% probability (magenta) compared to the entire F-star sample (black,top), globular clusters (blue, middle), and bulge stars (cyan, bottom). We note that the majority ofthe F-dwarf HVS candidates are extremely metal poor with only a couple relatively metal rich at [Fe/H]∼ −0.5. We caution, however, that the grid edge of the model atmospheres is at [Fe/H] = −2.5; anycandidate more negative than the vertical red line is to be ignored (Allende Prieto et al., 2014, privatecommunication).

94

Chapter V

CONCLUSION

In this thesis I described two complementary techniques to mine the Sloan Digital Sky

Survey (SDSS) data to search for stars that are unbound to the Milky Way.

First, we developed a technique to identify distant M-giant intragroup stars (IGSs)

within SDSS based solely on color. Using this technique, we identified 700 IGS candidates,

between 300 kpc and 2 Mpc (Palladino et al., 2012). These IGS may constitute rare tracers

of an underlying intracluster light (ICL) population surrounding the Milky Way. One

possible explanation for the origin of these IGS is that they were ejected from the center

of the Galaxy through interactions with our supermassive black hole as hypervelocity

stars (HVSs).

Secondly, we identified candidate HVSs from a sample of SEGUE G- and K-dwarfs.

We found that nearly half of the candidates exceed their escape velocities with at least

98% probability and no candidate’s orbit is consistent with a Galactic Center origin

(Palladino et al., 2014). The lack of HVS candidates originating from the Galactic Center

is an indication that either the ejection mechanism is mass-dependent or the initial mass

function at the center of the Galaxy is even more top-heavy than suggested in the literature

(e.g.; Figer et al., 1999, Section 3.6.4).

We plan to continue the search for stars that comprise the unbound stellar population

in the Milky Way. We are currently searching for HVS candidates in an extended G- and

K-type sample that includes both dwarfs and giants and probes regions of the Galaxy

beyond the disk. We are also searching for more HVS candidates within a sample of F-

stars, containing dwarfs and giants, to constrain the mass-dependence of the supermassive

black hole ejection mechanism operating at the center of the Milky Way.

96

Appendix A

ESTIMATION OF EXPECTED HVS VIA THE BINARY DISRUPTIONMECHANISM.

Here we estimate on the number of G/K-type HVS we should expect to observe within

SDSS resulting from the supernova binary disruption mechanism described in Section 1.4

and Tauris (2015).

In order to be consistent with the scenario described in Tauris (2015), we consider

only type Ia supernovae for this estimation. We begin with the known supernova rate of

1 supernova per 100 years and the ratio of type II to type Ia supernova of ∼ 3.5 (Sato

et al., 2007), which gives us a rate of 1 type Ia supernovae per 350 years. Then, adopting

an average velocity for our HVS candidates of 1,000 km/s, we determine it would take 5

million years for a star to travel from the disk to a distance of 5 kpc (consistent with our

observations). Therefore, over a period of 5 million years, we would expect approximately

14,000 type Ia supernovae in the Milky Way.

From here, we consider the fraction of the sky observed by SDSS, and determine that

there would be ∼ 3, 000 type Ia supernovae in the SDSS footprint from the past 5 million

years.

Since, by definition, type Ia supernovae exist in binary systems, we must consider

how many of these 3,000 binaries contain a low mass companion. Standard population

synthesis models adopt a flat distribution for assigning the mass to the secondary stel-

lar component of binaries (Abt, 1983)– if we group all spectral types (O/B, A/F, G/K,

97

M/later), we will assume that roughly 1/4 of these binary systems contain G/K-type com-

panions. This assumption determines that we should expect ∼ 750 G/K-type companions

to type Ia supernovae within the SDSS footprint from the past 5 million years.

According to Tauris (2015), only 1% of binary disruption scenarios with a low mass

companion will result in an ejection speed of v > 600km/s. This velocity requirement

yields that we should expect to observe O(10) low mass HVS from a supernova binary

disruption scenario within the SDSS footprint, which is consistent with our result of 20

candidates.

98

Appendix B

EXPANSION ON THE EXPECTED IGS CALCULATION.

Here we elaborate on the calculation outline in Section 2.5 determining the expected

number of IGS in the SDSS footprint.

If we assume that the SMBH in our galaxy had a merger with an intermediate mass

black hole (IMBH) with mass 3 × 105M�, it would 3-body scatter stars and eject them

from the system isotropically. This means that the total mass of ejected stars will also

be 3 × 105M� (Yu & Tremaine, 2003). Assuming an average stellar mass of 1 M�, then

3× 105 stars will be ejected.

The total sky has 41,253 square degrees, which yields approximately 7 ejected IGS per

square degree. Assuming the IGS formed 10 Gyr ago with a Salpeter IMF, then there

would be 0.00124 red giant HVS per square degree. The area of sky observed by SDSS

is 8000 square degrees, so this yields the expected tens of red giant IGS in the SDSS

footprint resulting from SMBH ejection.

99

Appendix C

IGS CANDIDATES REMAINING AFTER ALL CRITERIA CUTS.

100

Table C.1. Complete and unabridged.

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

758882136836343139 60.5013 80.8760 24.4 1.3 24.7 0.6 24.3 0.7 22.0 0.2 20.3 0.2 2.3 1.7758882137910740030 62.9212 82.5298 25.2 1.2 25.0 0.6 23.2 0.4 21.0 0.1 19.6 0.1 2.2 1.4758882626993718584 63.3170 81.6950 26.5 0.6 24.8 0.6 25.3 0.7 22.0 0.2 20.3 0.2 3.3 1.6758877527803168329 94.6323 63.7038 25.1 0.9 24.1 0.3 24.5 0.5 21.2 0.1 19.8 0.1 3.3 1.4758877527266231607 94.8017 63.2633 24.6 0.7 24.4 0.5 24.5 0.6 21.8 0.1 20.4 0.1 2.7 1.4758877527266493955 95.9369 63.5501 25.2 0.7 24.8 0.6 25.6 0.5 22.7 0.3 20.7 0.2 2.9 2.0758878272976455144 105.3459 66.8553 25.3 0.9 24.4 0.4 24.1 0.4 21.8 0.1 20.2 0.1 2.3 1.6758878271902778853 105.8427 66.0785 23.8 0.7 24.7 0.4 24.6 0.5 22.3 0.2 20.8 0.2 2.3 1.5758884768580109918 107.9936 38.3022 24.8 1.1 25.1 0.7 24.4 0.6 21.9 0.1 20.4 0.2 2.6 1.4587738067260998978 109.5721 39.4395 25.3 0.9 25.7 0.6 24.6 0.7 22.1 0.2 20.0 0.1 2.5 2.1587738066187126136 110.3269 38.8813 23.9 1.2 24.8 0.6 24.3 0.6 22.0 0.2 20.6 0.2 2.2 1.5758884821194311430 111.7235 31.6748 23.3 0.5 24.9 0.5 23.8 0.4 21.4 0.1 20.0 0.1 2.4 1.4758884803478619431 112.4325 31.0977 25.2 1.1 24.5 0.5 24.1 0.6 21.9 0.1 20.5 0.1 2.2 1.4587737808490071190 112.6070 38.1797 25.4 1.0 25.2 0.6 24.8 0.8 22.2 0.2 20.7 0.2 2.6 1.6587728906096674179 112.7248 27.9531 24.8 0.9 25.1 0.6 25.1 0.6 21.9 0.1 20.5 0.2 3.2 1.4587725551190869074 113.3506 36.8066 23.7 0.7 24.8 0.3 25.1 0.8 21.9 0.1 20.4 0.1 3.3 1.5587727866178372734 113.9236 31.5228 23.8 0.7 25.3 0.6 24.2 0.5 22.0 0.2 20.4 0.1 2.2 1.5587725552265790733 114.2540 39.4958 23.7 0.7 24.7 0.6 25.0 0.7 22.1 0.2 20.8 0.2 2.9 1.4587725775066563723 114.3135 39.3165 25.3 0.8 25.4 0.6 24.8 0.7 21.8 0.1 20.1 0.1 3.0 1.7588013382718391798 115.5088 23.9862 25.6 0.6 25.1 0.5 24.2 0.5 22.0 0.1 20.5 0.1 2.2 1.4587732152555078919 115.7199 22.3048 23.7 0.9 26.6 0.4 23.8 0.5 21.2 0.1 19.3 0.1 2.7 1.9587725775067677784 115.9952 41.5387 25.5 0.8 25.3 0.6 24.0 0.5 21.6 0.1 20.3 0.1 2.3 1.3587732054308947237 116.6473 26.0150 23.7 0.7 24.9 0.6 24.1 0.6 21.3 0.1 19.9 0.1 2.7 1.4587725774530872383 116.6594 41.4087 24.1 0.8 23.9 0.4 24.0 0.6 21.8 0.1 20.4 0.1 2.3 1.3588016878822295117 116.7229 18.5509 25.8 0.6 24.8 0.6 24.4 0.6 21.6 0.1 20.0 0.1 2.9 1.5587737826210219010 116.7903 45.1563 24.7 1.0 24.7 0.6 24.8 0.7 21.9 0.1 20.5 0.2 3.0 1.3587728906099623039 117.2504 33.4457 24.1 0.9 25.3 0.6 23.9 0.5 21.0 0.1 19.2 0.1 2.9 1.7

101

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587738372742121166 117.5023 18.4613 24.8 0.8 25.5 0.5 24.9 0.5 22.7 0.3 20.8 0.2 2.2 1.9588013383793771999 117.5227 27.3834 24.2 0.8 24.5 0.5 24.9 0.6 22.7 0.2 21.1 0.2 2.1 1.6587728906636952618 117.5359 34.5913 24.9 0.9 24.5 0.5 24.3 0.6 21.6 0.1 20.2 0.1 2.7 1.4587731679573509088 117.6023 27.9611 25.8 1.2 25.7 1.0 23.5 0.9 20.9 0.1 19.0 0.1 2.6 1.9587735043069707709 117.7701 20.8646 24.7 0.9 25.2 0.6 25.6 0.5 22.4 0.2 20.9 0.2 3.3 1.4587728931334653093 117.9390 33.6761 25.0 0.9 24.1 0.4 23.9 0.5 20.9 0.1 19.4 0.1 3.0 1.4587735043069969790 118.3476 21.2348 25.0 0.8 25.2 0.6 24.5 0.6 22.3 0.2 20.9 0.2 2.2 1.4587737809568531492 118.6204 48.1006 23.7 0.8 25.4 0.5 24.3 0.6 21.9 0.1 20.4 0.2 2.5 1.4588016878286406831 118.8410 19.7030 25.0 1.4 25.0 0.8 25.1 0.7 22.0 0.2 20.5 0.2 3.2 1.4587731873385481740 118.9846 32.3811 25.5 0.6 24.6 0.4 24.8 0.5 21.7 0.1 20.1 0.1 3.2 1.5587735235806561437 118.9877 21.3134 23.5 0.8 24.9 0.6 24.7 0.7 21.4 0.1 20.0 0.1 3.3 1.4587735236343759987 119.1972 22.2818 25.2 0.8 25.4 0.6 25.3 0.6 22.3 0.2 20.7 0.2 3.0 1.5587738066730484820 119.4568 52.3041 24.7 0.9 24.7 0.5 23.9 0.4 21.6 0.1 20.2 0.1 2.3 1.4758877528344757598 119.8005 65.7236 24.3 0.7 25.2 0.4 25.0 0.5 22.4 0.1 20.4 0.1 2.6 1.9587739115234788850 119.8104 17.9973 24.0 0.8 24.7 0.4 24.0 0.4 21.6 0.1 20.1 0.1 2.4 1.5587727867256243248 119.8520 39.6771 24.5 0.9 24.4 0.5 24.1 0.5 20.9 0.1 19.4 0.1 3.2 1.5587742010042287707 120.2735 10.3882 23.7 1.0 24.7 0.6 24.8 0.7 22.1 0.2 20.4 0.2 2.7 1.6588297863634682833 120.3658 24.4537 25.7 1.0 25.2 0.8 24.3 0.8 22.0 0.2 20.6 0.2 2.4 1.4587725470665081929 120.4194 43.3815 23.5 0.6 25.6 0.5 24.2 0.4 21.5 0.1 19.9 0.1 2.7 1.6587737826749645877 120.5762 50.4355 24.1 1.0 24.8 0.3 23.7 0.4 21.5 0.1 20.1 0.1 2.2 1.4587741708859803246 120.6010 12.5824 25.5 0.6 25.1 0.5 23.5 0.3 21.3 0.1 19.9 0.1 2.2 1.4587742010042549539 120.7911 10.6056 23.1 0.6 23.7 0.4 24.0 0.6 21.8 0.1 20.4 0.2 2.2 1.4588013382184469831 120.8817 28.7355 23.8 0.4 25.0 0.6 25.7 0.4 22.9 0.2 21.1 0.2 2.8 1.8587732469846377586 120.9695 26.5794 25.7 0.8 24.0 0.4 23.6 0.4 20.9 0.1 19.5 0.1 2.7 1.4587745244689073605 121.0114 9.6150 24.5 0.8 24.5 0.4 23.7 0.3 21.1 0.1 19.8 0.1 2.5 1.3587728669878912102 121.1313 40.8448 25.2 0.8 24.7 0.5 25.0 0.6 22.3 0.2 20.9 0.2 2.7 1.4588023046933120424 121.1645 13.0654 24.1 0.8 24.5 0.4 24.9 0.6 22.0 0.2 20.7 0.2 2.8 1.3

102

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587745243615266573 121.2201 8.7283 24.6 0.8 25.3 0.5 25.0 0.5 21.8 0.1 20.2 0.1 3.3 1.6587739115235509353 121.2323 18.8467 25.1 0.9 24.7 0.5 25.2 0.6 21.9 0.1 20.2 0.1 3.2 1.8587745403603453761 121.4298 8.4593 24.9 0.7 24.7 0.4 25.2 0.4 22.6 0.2 21.2 0.2 2.6 1.4587745402529711807 121.5256 7.7839 25.0 0.7 24.8 0.4 24.2 0.4 22.0 0.1 20.4 0.1 2.2 1.6587744637488596380 121.5423 11.1817 25.5 1.0 25.2 0.6 24.2 0.7 21.7 0.1 20.3 0.1 2.5 1.4587731520662930498 121.5799 31.5473 25.4 1.0 25.3 0.7 24.0 0.6 21.3 0.1 19.6 0.1 2.7 1.7587741387273275005 121.6111 16.0509 25.1 0.8 24.6 0.4 24.8 0.5 21.9 0.1 20.5 0.2 2.9 1.5587734623238227199 121.6396 26.8599 25.5 0.7 24.7 0.5 23.9 0.5 21.3 0.1 19.8 0.1 2.6 1.4587738066194465721 121.7083 53.7864 23.7 0.9 25.4 0.5 24.9 0.7 22.1 0.2 20.5 0.1 2.8 1.6587738372744217890 121.7230 21.3338 24.3 0.8 26.0 0.5 24.9 0.6 22.3 0.2 20.9 0.2 2.6 1.4587741532764898777 122.0871 14.6230 24.4 0.8 25.7 0.4 25.0 0.6 22.2 0.2 20.9 0.2 2.7 1.4587731887346025354 122.1712 36.4783 25.4 0.7 25.1 0.6 24.5 0.5 22.2 0.2 20.8 0.1 2.4 1.4587725550659240849 122.3177 46.7939 25.6 0.7 24.1 0.5 23.2 0.4 20.9 0.1 19.3 0.1 2.3 1.6587728906102506800 122.3662 38.6413 24.7 0.9 25.3 0.5 24.1 0.5 21.0 0.1 19.6 0.1 3.1 1.4587739377229628867 122.4993 18.3702 24.9 1.1 25.5 0.6 23.6 0.4 21.1 0.1 19.5 0.1 2.5 1.5587745243615921560 122.5645 9.1305 25.5 0.6 24.6 0.4 24.8 0.5 22.7 0.2 21.0 0.2 2.1 1.7587744874248799448 122.5791 9.5182 24.9 1.1 25.1 0.6 23.8 0.5 20.9 0.1 19.5 0.1 2.9 1.5587734621627614164 122.5965 25.8422 24.8 1.1 24.6 0.5 24.7 0.7 22.2 0.2 20.7 0.2 2.4 1.5587738565479368364 122.6182 7.3218 24.8 1.0 24.6 0.5 25.3 0.5 22.5 0.2 21.0 0.2 2.8 1.6587742010043467053 122.8561 11.3085 25.9 0.6 25.8 0.5 25.2 0.6 22.3 0.2 20.9 0.3 2.9 1.4588007005234004760 122.8710 45.4871 24.4 1.1 24.8 0.7 24.7 0.7 22.0 0.2 20.6 0.2 2.7 1.4587739153354851262 123.2158 19.9350 25.5 0.9 25.4 0.7 24.0 0.6 21.5 0.1 19.9 0.1 2.5 1.6587742008969790819 123.3029 10.5153 25.1 1.2 24.0 0.4 24.2 0.6 21.8 0.1 20.0 0.1 2.3 1.8587732471458694255 123.3611 30.2143 24.3 1.0 25.6 0.6 25.1 0.7 22.6 0.3 20.9 0.2 2.5 1.7587742009506792701 123.3705 11.1259 24.7 1.0 25.8 0.6 24.3 0.6 21.9 0.1 20.4 0.1 2.4 1.5587739153354916942 123.4933 19.9022 23.5 0.9 25.7 0.6 24.9 0.7 22.3 0.2 20.6 0.2 2.6 1.8587741386737255953 123.5510 16.6804 25.2 0.7 25.0 0.4 24.5 0.5 22.1 0.1 20.7 0.2 2.4 1.4

103

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587745403067565543 123.6343 8.6650 24.6 0.9 24.2 0.3 23.9 0.4 21.2 0.1 19.9 0.1 2.7 1.3587734949653120190 123.7966 6.6361 24.9 1.2 24.1 0.5 24.5 0.9 22.3 0.3 20.4 0.2 2.2 1.8587731522275312616 123.8046 35.2063 24.6 1.1 25.7 0.5 25.4 0.7 22.2 0.2 20.6 0.2 3.2 1.6587745244690384353 123.8545 10.4778 25.0 0.7 25.1 0.5 23.9 0.4 21.7 0.1 20.3 0.1 2.1 1.5588016878825964493 123.8681 23.6659 25.1 1.2 23.9 0.4 23.9 0.6 21.2 0.1 19.6 0.1 2.7 1.7587735236346315834 124.2462 25.9692 25.5 0.8 25.9 0.6 25.7 0.7 22.7 1.0 20.8 0.2 2.9 1.9587734949653382475 124.4021 6.8419 23.4 0.7 24.4 0.6 24.0 0.7 21.8 0.2 20.2 0.2 2.2 1.6587742008970380597 124.5343 11.0003 25.2 1.2 25.1 0.6 24.0 0.5 21.9 0.1 20.5 0.1 2.2 1.3588016879363359634 124.5851 24.7195 23.2 0.6 25.5 0.6 23.8 0.5 21.5 0.1 20.1 0.1 2.3 1.4588010358525134744 124.6703 1.9613 24.7 1.2 25.5 0.6 25.2 0.5 22.7 0.2 20.7 0.2 2.5 2.0587735236883645397 124.8579 26.9178 25.4 0.9 25.3 0.6 25.3 0.7 22.0 0.2 20.4 0.2 3.2 1.7587738948271473620 125.1085 23.5913 25.0 1.1 25.5 0.6 24.5 0.7 22.0 0.2 20.6 0.2 2.5 1.3588016839634584912 125.2505 23.8631 25.8 0.7 25.3 0.6 23.5 0.3 21.3 0.1 19.7 0.1 2.2 1.6587737808497673062 125.4675 53.0010 25.4 1.1 24.6 0.6 24.6 0.9 21.3 0.1 19.7 0.1 3.3 1.6587735235809969032 125.5140 26.3690 23.9 1.1 25.9 0.5 23.9 0.6 21.7 0.1 19.9 0.1 2.3 1.7587741816771773524 125.5536 13.5298 26.0 0.7 24.1 0.4 24.4 0.6 22.2 0.2 20.8 0.2 2.2 1.5587739152819029103 125.7847 20.7065 25.9 1.0 26.5 0.9 24.8 0.7 22.3 0.2 20.9 0.2 2.5 1.4587741532229731745 125.8905 16.0249 24.1 1.0 25.1 0.6 24.3 0.6 21.7 0.1 19.8 0.1 2.6 1.9587731885736723588 125.9387 37.9468 24.1 1.0 25.3 0.6 25.0 0.6 22.1 0.1 20.8 0.1 2.9 1.4588016879901017043 125.9927 26.2273 23.8 0.8 25.0 0.7 24.3 0.6 21.8 0.1 20.1 0.1 2.6 1.7587741387812373747 126.0358 18.8876 25.2 0.6 25.3 0.4 24.4 0.5 21.9 0.1 20.0 0.1 2.5 1.9587732701777364516 126.4451 3.4755 23.6 0.9 25.2 0.7 24.1 0.6 22.0 0.1 20.6 0.2 2.1 1.4587739376157590638 126.4929 19.4975 23.4 0.7 24.7 0.6 24.1 0.5 21.7 0.1 20.3 0.1 2.4 1.4587741817309234100 126.8135 14.3474 23.8 0.8 24.7 0.6 23.5 0.4 21.2 0.1 19.8 0.1 2.3 1.4587734621629776894 126.9443 29.0573 25.3 1.0 24.1 0.4 23.5 0.4 21.0 0.1 19.7 0.1 2.5 1.4588848899352561319 126.9608 -0.5883 24.8 1.0 24.8 0.6 23.7 0.4 21.5 0.1 20.1 0.1 2.2 1.5758877529419810240 127.3261 66.1607 24.4 0.7 25.3 0.4 23.5 0.3 20.9 0.1 19.1 0.0 2.5 1.8

104

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

588010358526444861 127.6105 2.2769 24.4 1.4 25.1 0.7 24.2 0.6 21.6 0.1 20.0 0.1 2.6 1.6587742008971887729 127.7826 12.1561 23.8 1.0 25.5 0.6 24.7 0.6 22.0 0.1 20.5 0.1 2.7 1.6588848900426761686 127.9468 0.2102 23.6 0.6 24.4 0.5 24.8 0.6 22.2 0.2 20.8 0.2 2.6 1.4758885526635152958 128.0022 -3.5678 24.2 1.0 24.4 0.4 24.3 0.6 21.1 0.1 19.5 0.1 3.2 1.6587741709937149050 128.0561 16.6285 23.3 0.4 25.3 0.5 24.3 0.6 21.3 0.1 19.7 0.1 3.0 1.5587739406759560244 128.1348 20.5569 24.8 1.0 24.2 0.4 24.8 0.8 21.5 0.1 20.1 0.1 3.3 1.5588013382188270667 128.2241 34.6591 25.2 0.9 24.7 0.5 24.1 0.4 21.7 0.1 20.1 0.1 2.4 1.6587735343181989199 128.2882 6.4828 24.2 1.0 25.7 0.4 24.9 0.5 22.3 0.2 20.8 0.1 2.7 1.5587739115775985007 128.5542 23.6851 23.8 0.7 24.8 0.5 24.1 0.4 21.6 0.1 20.1 0.1 2.5 1.5587739406222820115 128.5628 20.3347 24.2 1.2 25.9 0.5 23.6 0.5 21.0 0.1 19.5 0.1 2.5 1.6587725552273458067 128.6043 54.1334 24.9 1.1 24.5 0.6 24.7 0.8 21.8 0.2 20.4 0.2 3.0 1.4587727900001437041 128.7573 0.7449 24.4 1.1 24.6 0.6 24.3 0.5 22.0 0.1 20.1 0.1 2.3 1.9588010136263263191 129.1525 47.2654 25.0 0.9 24.1 0.5 23.9 0.5 21.7 0.1 20.3 0.2 2.2 1.4587735240099890134 129.1914 28.7956 24.4 1.3 24.1 0.6 24.6 0.7 22.1 0.2 20.8 0.2 2.5 1.3587745243618936116 129.2938 11.3592 25.0 0.9 24.7 0.5 25.2 0.5 22.7 0.2 20.7 0.2 2.5 2.0587732702315611255 129.5683 4.1795 24.8 1.1 25.7 0.8 23.8 0.5 21.0 0.1 19.2 0.1 2.7 1.8588017979409171295 129.7783 26.2118 25.6 0.6 24.5 0.5 25.1 0.6 22.3 0.2 20.8 0.2 2.9 1.5587744637492462684 130.0276 14.4030 23.2 0.7 25.7 0.5 24.1 0.7 22.0 0.1 20.6 0.2 2.1 1.5587741532768634037 130.1910 18.3188 24.6 0.9 25.2 0.5 24.1 0.5 21.4 0.1 19.7 0.1 2.7 1.7588023239936181347 130.8433 15.1661 24.7 0.9 24.9 0.6 23.5 0.3 21.2 0.1 19.9 0.1 2.2 1.4588010360138499214 130.8541 3.6405 25.7 0.8 25.4 0.7 23.7 0.5 21.2 0.1 19.9 0.1 2.4 1.3587735343183168623 130.9081 6.8343 25.5 0.8 24.2 0.4 24.6 0.6 22.2 0.2 20.2 0.1 2.5 2.0587738947200287788 130.9399 26.1878 24.5 1.0 25.5 0.6 24.5 0.6 22.3 0.2 20.9 0.2 2.2 1.3588023239130940550 131.1204 14.8844 24.3 1.1 25.2 0.6 23.6 0.9 21.4 0.1 19.5 0.1 2.2 1.9587732048940958642 131.1430 41.9367 24.5 1.4 25.1 0.5 24.1 0.6 21.9 0.1 20.3 0.1 2.2 1.7587732578297316598 131.4154 4.5721 23.5 0.6 25.5 0.4 24.9 0.5 22.6 0.2 20.5 0.1 2.3 2.1587731885739410417 131.7574 42.1904 24.9 1.3 25.2 0.6 24.5 0.7 22.3 0.2 20.8 0.2 2.1 1.5

105

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

588016879367095353 132.6092 29.4826 23.6 0.8 25.2 0.6 24.6 0.6 21.9 0.1 20.6 0.2 2.7 1.3587745243083638011 132.8636 11.8510 23.8 0.9 26.4 0.4 23.6 0.4 21.4 0.1 19.9 0.1 2.2 1.5587745244157445136 132.8730 12.7470 24.2 1.0 25.3 0.5 24.3 0.6 22.2 0.2 20.8 0.3 2.2 1.4587734623243994049 133.7811 35.0230 25.2 0.8 24.6 0.6 24.3 0.7 22.0 0.2 20.0 0.1 2.3 2.0587741390494172383 133.7948 20.9534 24.7 1.0 25.3 0.5 25.2 0.5 22.2 0.1 20.7 0.2 3.0 1.5587739115241407869 133.8194 25.8542 24.9 0.9 24.7 0.5 24.6 0.5 22.4 0.1 20.9 0.2 2.2 1.5587738067810517573 134.0615 64.5391 25.2 0.9 24.8 0.5 23.5 0.3 21.4 0.1 20.0 0.1 2.2 1.4587728880868459565 134.1800 3.7857 25.6 0.8 25.3 0.7 24.8 0.7 22.2 0.2 20.7 0.2 2.6 1.5587728931879781318 134.3119 48.0796 24.0 0.9 25.9 0.5 24.2 0.6 22.0 0.1 20.5 0.2 2.3 1.5587738065662444681 134.9270 62.3799 24.5 1.0 26.1 0.5 25.4 0.6 22.4 0.2 20.8 0.2 2.9 1.6587725551201682191 135.0932 56.9195 23.9 1.0 25.2 0.7 24.3 0.7 21.3 0.1 20.0 0.1 3.0 1.4588848900966974589 135.5404 0.7874 25.3 0.7 24.5 0.6 24.8 0.6 22.6 0.3 20.8 0.2 2.2 1.8588010931370787667 136.2548 -1.1901 25.9 0.9 25.9 0.8 23.9 0.8 21.1 0.1 19.6 0.1 2.8 1.5587725074990892118 136.4803 0.0084 24.8 0.8 24.1 0.4 23.5 0.4 21.1 0.1 19.7 0.1 2.5 1.3587739157111767895 136.4962 26.2652 23.1 0.7 24.9 0.6 23.4 0.4 21.1 0.1 19.5 0.1 2.3 1.6587731887352513242 136.4992 46.7866 23.3 0.7 25.5 0.7 24.3 0.8 21.6 0.1 20.1 0.1 2.6 1.6587735661006685535 136.6245 30.3807 25.2 0.8 24.9 0.5 24.6 0.6 22.1 0.1 20.7 0.1 2.5 1.5587731521207075766 136.6842 43.0042 25.0 1.1 25.1 0.6 24.7 0.8 21.8 0.2 20.5 0.2 2.8 1.4587737810113070028 137.0808 62.1737 25.4 0.7 24.5 0.4 25.0 0.7 21.9 0.1 20.4 0.1 3.1 1.5588848899893953565 137.2123 -0.1872 25.2 0.7 24.7 0.6 24.7 0.6 21.7 0.1 20.3 0.1 3.0 1.5587726031692956510 137.2299 0.9463 24.0 1.4 25.7 0.7 24.2 0.6 22.0 0.2 20.5 0.2 2.2 1.5587732771572941745 137.6327 6.8926 23.8 0.9 24.5 0.5 24.2 0.6 21.7 0.1 20.2 0.2 2.5 1.5588010360141644747 137.9911 4.1146 25.6 0.7 25.9 0.5 23.2 0.3 20.9 0.1 19.4 0.1 2.3 1.5587732578837267406 138.4298 5.7164 25.2 0.9 25.8 0.6 24.8 0.8 21.9 0.2 20.5 0.1 2.9 1.4587745402000376763 138.6059 11.5764 25.0 1.2 25.4 0.6 24.9 0.6 22.3 0.2 20.5 0.1 2.6 1.8587745403611120842 138.7042 12.7301 24.4 0.8 24.6 0.5 23.4 0.3 21.0 0.1 19.6 0.1 2.4 1.5588010931372229514 139.5752 -1.3058 24.8 1.4 24.7 0.8 25.0 0.9 21.9 0.2 20.5 0.2 3.2 1.3

106

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587739116317901722 139.6774 29.3276 24.7 1.0 24.8 0.5 23.7 0.4 21.6 0.1 20.2 0.1 2.1 1.4587739377237623666 139.9974 26.7931 25.1 1.0 24.0 0.4 25.0 0.6 21.8 0.1 20.4 0.2 3.2 1.4588009366936683268 140.1298 53.4593 23.9 1.0 25.3 0.6 24.6 0.7 22.1 0.2 20.2 0.2 2.5 1.8587741532236350353 140.7038 21.8742 25.0 1.0 25.3 0.5 24.8 0.6 22.1 0.1 20.3 0.1 2.7 1.7588023046942032976 140.8789 20.6767 23.8 0.9 24.9 0.6 24.3 0.5 22.0 0.1 20.6 0.2 2.3 1.4587742062128530595 141.0222 17.1453 25.0 0.8 26.0 0.4 24.8 0.6 22.5 0.2 21.0 0.2 2.3 1.5587735661008782311 141.4131 32.7343 24.5 0.9 25.3 0.5 25.1 0.5 22.5 0.2 21.2 0.2 2.5 1.4587725084112126989 141.8161 -1.2311 24.9 0.9 23.9 0.3 24.7 0.7 21.8 0.1 20.2 0.1 2.9 1.6587732048408216470 141.9283 47.6861 25.3 1.0 26.1 0.5 23.4 0.4 20.9 0.1 19.6 0.1 2.5 1.3587741816779048079 142.0450 18.8744 24.1 0.9 25.2 0.4 23.6 0.3 20.8 0.0 19.3 0.1 2.8 1.6587725082501710856 142.2355 -2.5049 23.1 0.5 25.2 0.7 24.9 0.6 22.1 0.1 20.5 0.1 2.8 1.6587742061055509536 142.9936 16.6777 23.6 0.6 25.3 0.5 23.4 0.3 21.3 0.1 19.6 0.1 2.1 1.7587741490361992228 143.6895 23.6026 24.5 0.9 24.9 0.5 24.2 0.4 21.7 0.1 20.2 0.2 2.5 1.6588009368548868956 143.8196 56.6921 25.0 1.2 24.5 0.5 25.1 0.8 22.0 0.2 20.3 0.2 3.1 1.8587741821600007462 143.8346 20.0941 25.0 0.6 24.9 0.4 25.5 0.4 23.2 0.3 21.2 1.0 2.3 2.1587745541052171128 143.8352 14.0716 24.0 0.7 25.2 0.5 25.1 0.7 22.3 0.2 21.0 0.2 2.7 1.3587735239569244837 143.8536 35.9067 24.6 0.9 25.0 0.8 24.2 0.6 21.2 0.1 19.9 0.1 3.0 1.3587735241717253077 144.2055 37.9672 24.1 0.7 25.3 0.5 24.9 0.6 22.7 0.3 21.1 0.2 2.2 1.5587741532774990849 144.5733 23.6227 25.2 0.8 24.7 0.5 25.3 0.6 22.3 0.2 20.2 0.1 3.0 2.1587725469600514982 144.7247 58.0650 23.3 0.5 24.1 0.4 24.7 0.7 22.1 0.2 20.6 0.2 2.6 1.5588010135194960753 144.8458 54.8227 25.2 1.0 24.8 0.6 23.5 0.4 21.2 0.1 19.8 0.1 2.4 1.3587746028521653096 145.0208 80.8068 24.9 1.7 25.6 0.9 25.1 1.0 22.0 0.2 20.3 0.2 3.1 1.7587735347484492866 145.4473 11.0259 23.5 0.6 24.9 0.5 24.7 0.5 21.8 0.1 20.1 0.1 2.9 1.7587745245236888254 145.6147 16.5869 23.9 0.9 24.3 0.4 24.3 0.6 20.9 0.1 19.6 0.1 3.3 1.4587729149307519797 145.7727 -2.8949 24.1 1.1 24.4 0.8 24.3 0.9 21.7 0.2 20.0 0.1 2.6 1.7588010135732225093 145.8303 55.6668 23.0 0.4 24.6 0.6 24.2 0.5 21.7 0.1 20.2 0.1 2.4 1.6587745964634277002 146.0568 80.7485 25.6 1.1 24.3 0.5 25.3 0.9 22.2 0.2 20.1 0.1 3.1 2.1

107

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587742062130823973 146.4056 18.4595 25.1 0.8 25.1 0.7 24.0 0.4 21.6 0.1 20.2 0.1 2.4 1.4587739114172974115 146.6519 30.3160 25.6 0.8 25.1 0.6 23.3 0.3 21.2 0.1 19.3 0.0 2.1 1.9587745404151661507 147.1223 14.8640 25.0 0.9 25.4 0.5 24.0 0.5 21.4 0.1 19.9 0.1 2.6 1.5587729387680760562 147.1262 54.4118 25.5 0.7 25.3 0.7 23.9 0.5 21.8 0.1 20.0 0.1 2.2 1.7587725082503873175 147.1817 -2.6797 24.0 1.3 25.6 0.9 23.6 0.5 21.2 0.1 19.5 0.1 2.4 1.7587739407304885266 147.3420 29.0520 25.6 0.7 24.4 0.5 24.9 0.7 21.9 0.1 20.4 0.2 3.0 1.5588016892783755943 148.5550 37.3050 25.6 0.7 25.1 0.6 23.9 0.6 21.7 0.1 20.2 0.1 2.2 1.5587739377778164705 148.6406 30.2270 25.8 0.6 24.3 0.5 23.5 0.4 21.4 0.1 20.0 0.1 2.1 1.4587731500257903502 149.5388 52.1156 25.5 0.8 24.4 0.4 23.5 0.3 21.0 0.1 19.4 0.1 2.6 1.6587732771041313734 149.6479 7.8360 25.0 1.0 24.3 0.5 23.4 0.3 21.0 0.1 19.7 0.1 2.4 1.3587734622176346991 149.6934 41.2482 24.1 1.0 24.3 0.4 24.0 0.7 21.8 0.2 20.5 0.2 2.2 1.4587738410862183251 150.0329 12.6704 23.7 0.9 23.8 0.3 23.9 0.5 21.3 0.1 20.0 0.1 2.5 1.4587732049484907326 150.0537 52.0423 24.2 0.9 24.8 0.6 24.2 0.6 21.6 0.1 20.0 0.1 2.6 1.6588848900436788207 150.8812 0.2572 25.5 0.6 24.2 0.4 23.9 0.4 21.5 0.1 20.2 0.1 2.4 1.3587741491438879653 151.0424 26.5829 25.1 0.9 25.0 0.5 23.8 0.4 21.6 0.1 20.1 0.1 2.2 1.5587731500795429936 151.2333 53.2276 25.6 0.7 25.4 0.5 23.8 0.4 21.7 0.1 19.9 0.1 2.2 1.7587735661012780068 151.5337 36.5869 24.5 1.0 25.1 0.5 23.4 0.3 21.1 0.0 19.3 0.0 2.3 1.8587746028522308335 151.8511 79.8267 25.6 1.2 26.5 0.5 24.1 0.8 21.0 0.1 19.5 0.1 3.0 1.6587735661012911027 152.0080 36.6516 25.0 0.9 24.7 0.5 24.7 0.5 22.0 0.1 20.6 0.1 2.7 1.4587741815709762781 152.7671 20.7417 24.9 0.9 24.3 0.3 23.2 0.2 20.8 0.0 19.5 0.1 2.4 1.4587745401469863009 153.3206 13.9345 22.9 0.3 25.3 0.7 23.7 0.4 21.2 0.1 19.7 0.1 2.5 1.5587733079193813860 153.6774 49.4685 22.4 0.3 25.2 0.9 24.0 0.7 21.7 0.1 20.3 0.1 2.4 1.4587739376706323289 153.8388 30.7842 25.3 0.9 24.2 0.4 24.4 0.7 22.0 0.1 20.6 0.2 2.4 1.4587738618093962166 154.5962 34.5953 24.9 1.2 24.1 0.4 24.8 0.7 22.1 0.2 20.3 0.1 2.7 1.7587734623788991419 154.6451 44.3487 25.3 0.9 24.9 0.5 23.5 0.3 21.3 0.1 20.0 0.1 2.2 1.3587728879803827157 155.0198 3.9675 24.5 0.9 24.5 0.6 24.6 0.6 22.3 0.2 20.8 0.2 2.3 1.5588023046411125759 155.0974 23.9575 25.5 0.6 24.4 0.4 23.9 0.4 21.6 0.1 20.1 0.1 2.3 1.5

108

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587735661014287541 155.7114 37.7758 23.9 0.8 25.0 0.5 24.3 0.6 21.5 0.1 19.7 0.1 2.8 1.8587731500260066168 157.0133 54.2306 23.8 0.8 25.6 0.5 23.5 0.4 20.9 0.1 19.3 0.1 2.7 1.6587732482741568799 157.5530 46.1316 24.7 0.9 24.8 0.4 23.5 0.3 21.1 0.1 19.5 0.1 2.4 1.6587734863221883710 157.9937 9.2045 25.9 0.6 25.2 0.6 24.3 0.6 21.6 0.1 19.9 0.1 2.7 1.7588017605750096661 159.5751 42.8911 24.8 0.8 25.1 0.5 23.9 0.4 21.4 0.1 19.9 0.1 2.4 1.5587745539985179956 159.6697 15.7868 25.4 0.5 24.9 0.6 23.8 0.3 21.5 0.1 20.1 0.1 2.3 1.4587732578309702669 159.8156 7.0035 24.8 1.0 24.9 0.5 24.2 0.5 21.6 0.1 20.3 0.1 2.6 1.4587739407846802324 160.0626 32.8519 25.1 0.8 24.6 0.5 23.8 0.4 21.0 0.1 19.6 0.1 2.8 1.3587732578309833768 160.1011 6.8967 24.3 0.9 24.5 0.5 23.8 0.4 21.4 0.1 19.7 0.1 2.3 1.7587735348564788049 160.5537 13.7753 24.0 0.8 25.3 0.5 24.4 0.4 22.1 0.1 20.2 0.1 2.3 1.9587742863935997065 160.6133 15.4069 26.4 0.5 24.0 0.4 23.6 0.4 21.0 0.1 19.6 0.1 2.6 1.4588009370149061217 160.6377 58.9619 25.1 0.9 25.6 0.7 23.8 0.5 21.1 0.1 19.8 0.1 2.7 1.3588017978885014291 161.5637 37.6308 24.9 1.1 24.7 0.6 24.7 0.7 21.4 0.1 20.0 0.1 3.3 1.4587731498650567700 161.8517 54.0201 24.4 1.0 24.3 0.5 25.0 0.7 22.4 0.2 20.9 0.2 2.6 1.5588848900978770884 162.5416 0.7967 23.9 0.6 25.3 0.5 24.1 0.6 21.7 0.1 20.1 0.1 2.4 1.6588017111826367362 162.7343 45.7594 25.1 0.9 25.4 0.6 23.5 0.3 21.2 0.1 19.6 0.1 2.3 1.6587738615412360104 162.7542 34.2673 24.3 0.8 24.3 0.5 24.1 0.6 21.8 0.1 20.2 0.1 2.4 1.6587745517955974092 163.6358 -23.0362 23.9 1.6 25.6 0.7 24.5 0.8 22.1 0.2 20.2 0.1 2.5 1.8587741531709309855 164.6244 27.4117 25.7 0.8 25.1 0.7 23.4 0.4 21.0 0.1 19.3 0.1 2.4 1.7587726032241820432 164.6555 2.0157 23.1 0.6 24.3 0.5 24.7 0.7 22.5 0.3 20.4 0.2 2.2 2.1588011098872087170 164.9986 61.8172 24.9 1.2 25.3 0.7 23.8 0.6 21.2 0.1 19.8 0.1 2.6 1.4587739294550655835 165.0833 32.7535 24.4 1.2 25.5 0.5 24.8 0.6 22.1 0.2 20.7 0.2 2.7 1.4588017110216475538 165.4542 45.0014 24.2 1.1 25.1 0.6 24.8 0.7 22.2 0.2 20.6 0.2 2.6 1.6587745419172512941 165.5052 -20.0161 24.6 1.3 24.7 0.5 24.9 0.6 22.2 0.2 20.9 0.2 2.7 1.3587742949567759253 165.6178 62.9000 24.9 1.3 25.5 0.6 24.1 0.7 21.8 0.1 20.1 0.1 2.4 1.7588017720101962625 166.1909 40.1517 25.5 0.9 24.8 0.6 25.2 0.6 22.3 0.2 20.5 0.1 2.9 1.8587742061065405423 166.4210 21.0518 25.3 0.7 25.1 0.6 23.9 0.4 21.7 0.1 20.3 0.1 2.2 1.5

109

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587745419173299268 166.4666 -18.4174 24.4 1.6 24.9 0.6 23.9 0.4 21.5 0.1 20.0 0.1 2.4 1.5587739097519883343 166.5179 36.0247 25.0 1.0 25.1 0.6 23.5 0.9 20.8 0.0 19.4 0.1 2.7 1.4587745517421659160 167.3495 -18.3025 25.4 1.1 25.2 0.9 23.9 0.5 21.7 0.1 20.4 0.2 2.2 1.4588017702388368164 167.7542 10.9681 25.0 1.2 25.7 0.8 24.7 1.0 22.2 0.3 20.4 0.2 2.5 1.8588017627224015847 168.5089 44.2847 25.1 0.7 24.5 0.5 24.0 0.5 21.8 0.1 20.1 0.1 2.2 1.7587745421325763640 170.8485 -7.7415 24.5 0.9 24.5 0.4 23.9 0.4 21.7 0.1 20.0 0.1 2.2 1.8588010358008710228 171.3568 3.8177 23.3 0.5 24.7 0.6 23.2 0.2 21.0 0.1 19.3 0.0 2.2 1.7587726032781706246 171.5645 2.4977 24.1 1.2 23.5 0.3 23.9 0.5 21.7 0.1 20.2 0.2 2.2 1.5588017110755509046 172.2477 46.4072 23.9 0.8 24.6 0.5 23.7 0.4 21.2 0.1 19.6 0.1 2.5 1.6587748878767293348 172.4064 -4.6113 25.1 1.0 24.4 0.4 24.0 0.6 21.7 0.2 20.3 0.1 2.3 1.5588010878755930812 172.6794 4.6231 25.1 1.0 23.6 0.4 24.4 0.8 21.0 0.1 19.6 0.1 3.4 1.5587732772662215483 173.3376 10.7932 25.1 1.1 24.6 0.5 25.0 0.7 22.6 0.3 20.8 0.2 2.4 1.7587732483283551295 174.1708 49.3591 24.4 0.7 24.4 0.3 24.4 0.4 22.0 0.1 20.3 0.1 2.4 1.7587741709419676538 174.5612 27.4629 23.9 0.8 24.7 0.4 23.5 0.3 21.3 0.1 19.8 0.1 2.2 1.5587735349376451646 175.4564 15.3323 24.5 0.8 24.1 0.3 24.3 0.5 21.8 0.1 19.9 0.1 2.6 1.9587734894361904010 175.8093 10.9364 23.1 0.6 24.0 0.5 23.8 0.7 20.9 0.1 19.6 0.1 2.9 1.3588023668631536741 175.8511 19.2520 25.4 1.0 25.0 0.6 24.3 0.4 22.0 0.1 20.7 0.1 2.3 1.3587732771589850177 176.5640 9.9435 25.2 1.0 23.9 0.4 23.5 0.4 20.9 0.1 19.6 0.1 2.6 1.3587731869096477517 177.0183 54.6310 25.6 0.8 25.0 0.6 24.6 0.7 21.7 0.1 20.3 0.1 2.9 1.4587742572151440523 177.3201 19.6050 24.5 0.9 24.7 0.5 23.5 0.3 20.9 0.0 19.3 0.1 2.6 1.5588013381668373442 177.6184 51.0420 25.4 0.8 25.0 0.7 24.2 0.5 21.1 0.1 19.4 0.1 3.1 1.7587729386077750152 178.0388 59.0900 24.8 1.1 24.1 0.5 24.0 0.7 21.8 0.1 20.3 0.1 2.3 1.4587741602029831217 179.2004 27.5228 25.5 0.8 26.2 0.3 24.4 0.6 22.3 0.2 20.7 0.2 2.2 1.5588848900449436610 179.6998 0.2298 25.3 0.7 23.7 0.3 23.6 0.3 21.2 0.1 19.9 0.1 2.4 1.4588017979428438734 180.6327 40.3433 24.9 1.0 24.3 0.6 24.7 0.7 22.1 0.2 20.8 0.2 2.6 1.3587742189366609038 180.7011 24.2325 24.5 1.1 24.8 0.5 23.4 0.3 21.2 0.1 19.6 0.1 2.2 1.6587728676856660277 180.7489 63.7893 22.3 0.2 24.9 0.6 25.5 0.5 23.2 0.9 21.7 0.4 2.2 1.5

110

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

588017949350822800 181.0926 43.1136 26.1 0.9 24.3 0.3 23.7 0.4 21.5 0.1 19.7 0.1 2.1 1.8587742863676605501 182.0668 16.8712 25.2 1.1 25.0 0.5 23.6 0.4 21.0 0.1 19.5 0.1 2.6 1.5587732702875419575 182.1231 7.8887 25.6 1.0 24.5 0.5 24.0 0.5 21.3 0.1 19.9 0.1 2.8 1.4587741602031862746 184.3958 27.6086 24.3 1.0 24.9 0.5 23.4 0.3 21.3 0.1 19.9 0.1 2.1 1.4588013381670405094 185.0387 51.4017 24.9 0.9 25.2 0.6 23.8 0.4 20.8 0.1 19.0 0.0 3.0 1.9587741601495319326 185.2366 27.2104 25.5 0.6 24.8 0.5 23.3 0.3 20.9 0.1 19.6 0.1 2.4 1.3588017109685896049 185.9750 46.4380 25.3 0.9 25.7 0.6 25.2 0.6 21.8 0.1 19.9 0.1 3.3 1.9587725039557936262 186.5731 -3.2575 25.7 0.8 25.6 0.5 24.0 0.5 21.8 0.1 20.4 0.2 2.1 1.4587741602032976873 187.2962 27.6403 24.1 1.1 25.7 0.4 23.7 0.4 21.4 0.1 19.9 0.1 2.2 1.5587725040632071125 187.5061 -2.3313 25.1 0.8 24.1 0.4 23.4 0.3 21.0 0.1 19.5 0.1 2.3 1.5588017720645911348 187.5605 42.1361 24.8 1.1 25.2 0.5 24.3 0.6 21.8 0.1 20.3 0.1 2.5 1.5587731869099492352 189.0408 54.8202 23.6 0.9 24.5 0.7 23.3 0.3 21.1 0.1 19.7 0.1 2.3 1.4587732483287942155 189.8179 49.8006 23.7 0.6 25.4 0.5 24.4 0.6 21.2 0.1 19.7 0.1 3.2 1.6587742904474141884 190.4263 18.6385 25.8 0.5 25.0 0.5 24.6 0.6 21.9 0.2 20.2 0.1 2.6 1.8587732772132750451 190.6511 10.5235 26.0 0.9 25.0 0.6 25.3 0.6 22.3 0.2 21.0 0.2 3.0 1.4588017991220789974 190.9165 9.9436 25.5 0.9 24.1 0.4 24.1 0.6 21.7 0.1 20.3 0.1 2.4 1.4587738575141209378 190.9666 40.9319 23.6 0.5 25.1 0.4 25.0 0.4 22.4 0.2 20.9 0.2 2.6 1.4587745543729120325 191.7133 -13.2505 23.8 1.3 25.7 0.6 24.5 0.7 22.1 0.2 20.6 0.2 2.4 1.5587746041410552832 192.0253 -8.3185 24.0 1.0 25.4 0.7 24.9 0.7 22.3 0.2 20.9 0.2 2.6 1.4587742902327510145 192.3695 16.7756 25.2 0.8 24.5 0.4 24.9 0.5 22.4 0.2 20.9 0.2 2.6 1.5587742575908619510 192.6829 19.1709 24.9 1.1 23.7 0.3 23.5 0.3 20.9 0.0 19.5 0.1 2.6 1.4587732771596993679 193.1921 9.9646 25.9 0.6 24.9 0.6 23.3 0.3 21.1 0.1 19.7 0.1 2.2 1.4588023668639007562 193.9799 19.3382 24.7 1.3 24.3 0.4 24.4 0.5 21.3 0.1 19.9 0.1 3.0 1.5587741724971762568 194.2034 23.7828 24.5 0.8 25.1 0.6 24.9 0.6 21.7 0.1 20.2 0.1 3.3 1.5587739720291189639 195.6271 29.1829 24.9 1.1 25.2 0.6 24.4 0.6 21.4 0.1 19.4 0.1 3.0 2.0587733195697226654 195.8201 54.0262 25.5 0.9 25.1 0.6 24.8 0.7 22.1 0.2 20.3 0.1 2.7 1.8587728678470157331 196.2246 64.6864 23.7 0.8 24.3 0.5 24.3 0.6 21.6 0.1 20.1 0.1 2.8 1.5

111

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587742062151271483 196.3262 22.5705 24.6 1.1 25.4 0.6 25.2 0.5 21.8 0.1 20.5 0.1 3.3 1.4588017722260062969 198.7887 42.6726 25.4 1.2 24.8 0.6 24.1 0.6 21.7 0.1 20.3 0.1 2.4 1.4588018055645299778 199.3085 51.5645 24.6 0.8 24.3 0.3 24.8 0.5 21.8 0.1 20.4 0.1 3.0 1.4587736807225361346 201.7009 13.2873 24.3 1.0 25.0 0.7 24.2 0.5 21.9 0.1 20.6 0.2 2.2 1.3587725816953439053 201.7913 66.0372 23.6 0.8 24.1 0.3 24.2 0.7 21.1 0.1 19.3 0.1 3.2 1.7587729773680264258 202.0138 -2.3744 24.3 1.2 25.3 0.7 23.9 0.6 21.7 0.1 20.1 0.2 2.3 1.5588017991225574380 202.0260 9.4413 23.7 0.9 24.5 0.5 24.9 0.7 22.5 0.2 20.9 0.2 2.4 1.6587739504476357411 202.0431 30.4375 25.3 0.9 24.9 0.8 24.8 0.7 21.9 0.1 20.2 0.1 2.9 1.7587729776902079384 202.2706 -2.9269 25.7 1.0 23.6 0.4 24.2 0.7 21.9 0.1 20.5 0.2 2.3 1.4587741721216156530 202.4198 25.8089 25.3 0.9 25.2 0.6 23.6 0.4 21.3 0.1 19.4 0.1 2.3 1.9587726014005445549 203.3734 1.3577 25.2 1.0 24.5 0.7 23.4 0.3 21.1 0.1 19.6 0.1 2.3 1.5588017726019208408 203.7106 7.6235 25.4 0.7 25.3 0.5 25.0 0.6 22.5 0.2 20.7 0.1 2.4 1.8588017570317075482 204.1004 11.4837 25.1 0.8 25.1 0.6 24.6 0.6 22.4 0.2 21.0 0.2 2.2 1.4587739132951987468 204.4014 36.6419 25.2 0.6 25.0 0.4 24.1 0.4 21.9 0.1 20.3 0.1 2.2 1.6587729773681574984 204.9153 -2.1625 23.8 0.9 25.5 0.6 24.2 0.5 22.0 0.2 20.6 0.2 2.2 1.4587738574072317507 205.2519 38.5611 24.9 0.7 24.9 0.4 24.4 0.4 21.9 0.1 20.6 0.1 2.5 1.3588011219135431601 205.9093 61.4749 25.2 0.7 24.0 0.3 23.6 0.3 21.3 0.1 19.8 0.1 2.4 1.5587739707943027687 206.4155 28.6515 25.5 0.9 25.1 0.5 24.0 0.5 21.5 0.1 19.9 0.1 2.5 1.6587742060544918633 206.5629 20.3468 25.9 0.9 24.7 0.6 24.8 0.6 22.5 0.2 21.1 0.2 2.3 1.4587738574609647082 206.5928 38.7391 24.7 0.6 25.2 0.3 25.3 0.4 23.0 0.3 21.2 0.2 2.4 1.7587722981751915681 206.9856 -1.0598 24.3 0.8 25.1 0.6 24.0 0.4 21.8 0.1 20.0 0.1 2.2 1.8587746269582001411 207.0844 -3.5539 23.6 1.0 24.4 0.5 24.5 0.6 21.4 0.1 20.0 0.1 3.1 1.4587735696449209285 207.2544 55.4942 24.2 1.0 25.4 0.5 24.6 0.6 22.2 0.2 20.5 0.2 2.4 1.7587729774756561829 207.8376 -1.3271 25.6 0.8 24.4 0.6 23.9 0.5 21.4 0.1 20.0 0.1 2.5 1.4588017625089115043 207.9801 41.4142 25.0 0.9 24.9 0.7 24.3 0.5 21.6 0.1 20.2 0.1 2.7 1.4587746236297905182 209.0299 -6.4122 25.7 0.9 25.6 0.5 24.7 0.7 21.8 0.1 19.9 0.1 2.9 1.9587739406254277723 209.2927 31.8219 23.7 0.8 25.2 0.4 24.3 0.5 21.9 0.1 20.4 0.1 2.4 1.5

112

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587729159509705539 209.4048 4.8979 25.7 0.9 24.5 0.6 23.6 0.4 21.5 0.1 20.2 0.2 2.1 1.3587736586573120665 209.4356 40.8209 24.0 0.7 24.7 0.4 24.0 0.4 21.6 0.1 19.7 0.1 2.4 1.9588298664117994712 209.4619 45.5971 24.4 0.6 25.1 0.4 23.8 0.3 21.0 0.1 19.4 0.0 2.8 1.6587742594695693110 209.6562 16.8099 23.3 0.5 24.4 0.5 23.6 0.4 21.1 0.1 19.7 0.1 2.5 1.4587742592548537313 210.3118 15.0032 25.4 0.9 25.1 0.8 24.3 0.6 21.1 0.1 19.6 0.1 3.3 1.4588017991229244610 210.5254 8.9233 23.7 0.8 24.9 0.6 25.4 0.6 22.3 0.2 20.9 0.2 3.1 1.4588017991229310016 210.6635 8.9254 25.5 0.9 25.2 0.6 23.4 0.3 21.0 0.1 19.6 0.1 2.4 1.3587735695913321470 210.8686 54.3749 26.0 0.6 27.4 0.2 24.0 0.7 21.8 0.1 20.5 0.2 2.1 1.4588017992303838071 212.4217 9.5701 25.1 0.8 25.1 0.6 24.2 0.6 21.4 0.1 19.9 0.1 2.8 1.5587736478662656905 212.5009 11.6189 25.0 0.8 24.3 0.5 24.5 0.6 22.3 0.2 20.7 0.2 2.2 1.6588011219137004633 212.6382 60.1345 24.3 0.8 24.9 0.5 24.6 0.5 22.2 0.2 20.8 0.2 2.4 1.4587739380985562078 213.0207 31.6272 26.1 0.6 25.3 0.5 25.0 0.6 22.0 0.2 20.3 0.1 3.0 1.7587746278167282738 213.5916 -18.0786 23.1 0.9 25.6 0.7 23.9 0.7 21.7 0.1 20.1 0.1 2.2 1.7587739609175163770 213.6255 29.3398 24.7 1.2 25.2 0.5 24.3 0.6 21.9 0.1 20.1 0.1 2.4 1.9588848899927442575 213.6762 -0.1211 25.5 0.6 25.8 0.5 23.8 0.5 21.5 0.1 20.1 0.1 2.3 1.4587736542017750200 213.9824 8.3750 24.6 0.9 26.3 0.3 23.8 0.4 21.4 0.1 19.8 0.1 2.4 1.7588011123583091390 214.1712 59.0976 25.4 0.8 24.4 0.6 24.4 0.8 21.9 0.2 20.6 0.2 2.5 1.3587746278167938208 214.2849 -19.4582 23.9 1.8 26.3 0.5 25.4 0.8 22.0 0.2 20.7 0.2 3.4 1.4587736585501410737 214.8308 38.5935 23.8 0.6 24.5 0.3 24.1 0.3 21.8 0.1 20.0 0.1 2.3 1.8587742190454244421 215.2578 22.1226 25.3 1.0 25.2 0.5 25.0 0.5 22.3 0.2 20.6 0.2 2.6 1.7587736914602951670 215.2992 12.1341 23.2 0.5 25.5 0.6 23.3 0.3 21.0 0.1 19.7 0.1 2.3 1.3587736584428062095 215.5006 37.3992 24.1 0.6 24.1 0.3 23.6 0.3 20.9 0.0 19.5 0.1 2.7 1.4587730022789809162 215.5008 6.5153 24.9 1.3 25.5 0.6 23.9 0.5 21.7 0.1 20.2 0.2 2.2 1.5588017606304989959 216.2809 41.6769 25.8 0.8 24.5 0.5 23.5 0.3 21.0 0.1 19.6 0.1 2.5 1.4587736541481927841 216.3328 7.8922 23.4 0.7 24.5 0.4 23.4 0.3 21.0 0.1 19.7 0.1 2.4 1.3588017713661412643 216.6573 49.0901 25.6 0.7 25.1 0.4 23.7 0.3 20.8 0.1 19.1 0.0 2.8 1.7587733410984231821 218.0394 49.9561 23.6 0.7 25.2 0.6 23.8 0.5 20.8 0.1 19.1 0.0 2.9 1.7

113

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587733397562262461 218.1495 49.2996 24.0 1.2 24.1 0.4 24.2 0.7 21.5 0.1 20.0 0.1 2.8 1.5587739827129484142 218.6243 22.7365 25.4 1.2 25.6 0.5 24.1 0.5 21.3 0.1 20.0 0.1 2.7 1.3588298662510789880 218.8043 41.5426 23.8 0.6 25.0 0.3 24.6 0.4 22.5 0.2 20.4 0.1 2.1 2.1587736962922316671 219.5107 31.8622 24.7 0.9 24.9 0.5 24.5 0.6 22.3 0.2 21.0 0.2 2.2 1.3588017711515370532 220.0139 46.1570 24.8 1.0 25.3 0.5 24.2 0.4 22.0 0.1 20.3 0.1 2.2 1.6587739630630863931 220.8132 27.5135 25.3 0.9 24.7 0.5 23.7 0.4 21.5 0.1 20.1 0.1 2.3 1.3587742629061329898 221.6043 14.8235 25.1 0.9 24.2 0.4 24.3 0.6 22.1 0.2 20.6 0.1 2.1 1.5587722982295340447 221.9858 -0.7504 24.9 0.9 25.2 0.5 24.5 0.5 21.4 0.1 19.7 0.1 3.1 1.7587726032267052136 222.3068 1.6773 24.4 1.2 24.4 0.6 23.4 0.4 21.2 0.1 19.9 0.1 2.2 1.4588018055115703409 222.6902 45.3658 25.0 1.0 24.2 0.4 24.6 0.5 22.3 0.2 20.9 0.2 2.3 1.4587729776911123462 223.0024 -2.4566 24.6 1.5 25.7 0.6 24.0 0.5 21.9 0.1 20.4 0.2 2.2 1.5587735490821751827 223.3052 43.5829 23.6 0.5 24.4 0.4 23.3 0.2 20.9 0.1 19.5 0.1 2.3 1.4587736585504622197 223.3183 35.7665 23.7 0.5 25.2 0.3 23.8 0.3 21.1 0.1 19.2 0.0 2.6 2.0587729776911385690 223.6075 -2.4566 26.0 0.8 25.2 0.7 24.0 0.5 21.8 0.1 19.9 0.1 2.2 1.8587739827131974679 224.4462 21.0559 25.6 1.0 24.7 0.5 24.3 0.5 21.9 0.1 20.4 0.1 2.4 1.5588017979980907639 224.8475 33.7420 24.5 0.9 25.0 0.4 24.3 0.5 22.0 0.1 20.4 0.1 2.3 1.6588017702949880900 224.9550 9.1385 24.8 1.1 24.9 0.5 24.4 0.5 21.8 0.1 20.4 0.1 2.6 1.3588848899932554225 225.4619 -0.0569 25.3 0.7 24.9 0.4 24.9 0.6 22.3 0.2 20.8 0.2 2.6 1.5587739131349632328 225.6101 29.7374 25.9 0.5 24.8 0.4 23.9 0.3 20.9 0.0 19.3 0.0 3.0 1.6587739382064350410 225.8459 28.7320 23.8 0.7 25.0 0.4 24.9 0.5 21.8 0.1 20.1 0.1 3.1 1.7587739707950957500 225.9034 23.8605 24.9 1.1 25.3 0.5 24.6 0.6 22.2 0.2 20.5 0.2 2.4 1.7587742061090112393 226.3155 16.9165 24.6 1.0 25.0 0.5 23.9 0.4 21.8 0.1 20.5 0.1 2.1 1.3587742782061151186 226.3166 66.5927 24.7 1.5 25.3 0.6 25.0 0.7 22.1 0.2 20.7 0.2 2.8 1.4587739810492187739 226.4236 21.1685 25.3 0.7 23.9 0.3 24.2 0.4 21.5 0.1 20.1 0.1 2.6 1.4587729228758057768 226.4657 61.8045 25.3 0.9 24.8 0.6 24.7 0.7 22.1 0.2 20.5 0.1 2.5 1.6587736975270610131 226.9655 28.8498 25.3 0.9 24.8 0.5 23.3 0.2 21.1 0.1 19.8 0.1 2.2 1.3588017605772248021 227.2607 37.3744 24.1 0.9 25.9 0.4 24.6 0.6 22.2 0.2 20.9 0.2 2.4 1.3

114

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587726100415775772 227.5137 2.9317 24.5 1.7 24.9 0.8 23.7 0.5 21.2 0.1 19.8 0.1 2.5 1.4587742610269472024 227.7051 12.5743 25.2 0.9 24.3 0.4 23.5 0.3 21.1 0.1 19.4 0.1 2.4 1.8587733412061119193 228.1641 47.1411 24.4 1.1 25.5 0.6 24.7 0.7 21.8 0.2 20.4 0.1 2.9 1.4588017990700303528 228.5661 6.7330 23.7 0.9 24.6 0.6 24.6 0.6 21.9 0.1 20.4 0.1 2.8 1.4587739720304493641 228.7774 22.4037 25.5 0.8 24.6 0.5 23.5 0.4 21.3 0.1 19.9 0.1 2.3 1.4588017626707199080 228.8637 35.9400 25.0 0.9 25.1 0.4 23.8 0.3 21.6 0.1 19.9 0.1 2.2 1.7587729227148624895 229.2771 59.1033 25.3 1.1 24.3 0.5 24.4 0.7 21.4 0.1 20.0 0.1 2.9 1.4587735667458310997 229.2816 49.6756 25.8 0.8 25.2 0.6 23.5 0.3 21.2 0.1 19.8 0.1 2.3 1.4587739720304886838 229.6108 21.9413 23.9 0.9 25.1 0.5 24.1 0.4 21.3 0.1 19.7 0.1 2.9 1.5587729746838029514 230.4316 1.0337 24.6 1.4 24.6 0.6 23.3 0.3 21.0 0.1 19.6 0.1 2.3 1.3587736478670521399 230.5734 9.3747 24.6 0.7 24.9 0.5 25.0 0.6 22.1 0.2 20.6 0.1 2.9 1.5587733411525559181 231.3260 45.0889 26.0 0.7 24.6 0.5 24.9 0.6 22.1 0.1 20.7 0.2 2.8 1.4587733427626967884 231.5140 49.0118 23.8 1.0 24.8 0.6 23.6 0.3 21.5 0.1 20.0 0.1 2.1 1.5587739811568026947 231.6018 20.3935 25.2 0.6 25.2 0.4 24.5 0.4 22.1 0.1 20.8 0.2 2.4 1.3587739845389386773 231.6261 18.0976 25.1 0.9 24.1 0.3 24.3 0.4 21.5 0.1 19.9 0.1 2.7 1.6587742629065851966 231.9400 12.6672 24.9 1.0 25.2 0.5 25.3 0.6 22.3 0.2 20.8 0.2 3.0 1.5587729159519601807 232.0062 3.6837 24.1 1.0 25.1 0.7 24.4 0.6 22.0 0.2 20.5 0.2 2.4 1.5587742628529374488 232.8739 12.0835 22.7 0.4 25.2 0.5 24.9 0.6 22.0 0.1 20.5 0.2 2.9 1.5588017703490356395 233.2395 8.2607 23.8 0.9 25.3 0.6 24.2 0.5 21.9 0.1 20.5 0.1 2.3 1.4587735489215398938 233.4104 37.4698 24.6 1.2 24.8 0.5 25.1 0.7 22.0 0.2 20.7 0.2 3.1 1.3587736584972141961 233.8093 30.7206 24.8 0.7 24.9 0.4 25.0 0.4 22.4 0.1 21.0 0.2 2.6 1.4588011217533076244 233.9039 50.5680 26.2 0.5 25.3 0.6 24.4 0.6 21.8 0.1 20.4 0.1 2.6 1.3587739131353236873 233.9560 26.2114 25.1 0.9 24.9 0.5 23.3 0.2 21.0 0.0 19.7 0.1 2.3 1.3587729229296894714 234.0202 59.1885 23.7 1.0 24.9 0.7 24.4 0.7 21.2 0.1 19.9 0.1 3.2 1.3587736542026532135 234.0643 6.1930 24.9 0.9 25.3 0.5 23.3 0.3 21.1 0.1 19.6 0.1 2.2 1.5588017991239533745 234.0934 6.3800 24.9 1.4 24.9 0.7 24.2 0.7 21.9 0.1 20.5 0.2 2.3 1.4588011219679904764 234.0954 52.7817 22.6 0.3 24.4 0.4 24.3 0.5 21.9 0.1 20.5 0.2 2.4 1.4

115

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587739849672885314 234.2626 61.2775 25.3 1.0 24.7 0.5 25.0 0.6 22.3 0.2 21.0 0.3 2.7 1.3587729407535023060 234.7772 53.2424 24.0 1.3 25.2 0.6 24.1 0.6 21.4 0.1 19.8 0.1 2.7 1.6587733604262217093 234.9250 48.0162 25.0 0.8 25.4 0.4 25.3 0.4 23.0 0.2 20.9 0.2 2.4 2.0587729748450608329 234.9880 2.0907 24.5 1.0 24.6 0.5 23.5 0.4 20.9 0.1 19.4 0.1 2.6 1.5588018090541581454 235.0644 35.0280 24.2 1.0 25.1 0.5 23.7 0.4 21.0 0.1 19.6 0.1 2.7 1.4587736543100798537 235.4796 6.8844 23.6 0.5 25.0 0.5 23.7 0.3 21.4 0.1 20.0 0.1 2.2 1.4587736752465708166 235.5902 36.6984 25.1 1.0 24.9 0.6 24.6 0.6 22.2 0.2 20.9 0.2 2.4 1.3588011217533731867 235.6902 49.4629 24.6 1.3 24.6 0.5 24.7 0.7 22.3 0.2 20.5 0.2 2.3 1.8587729158984303831 235.6940 3.1472 23.9 0.9 24.5 0.7 23.6 0.4 21.2 0.1 19.8 0.1 2.4 1.4587739815314785389 235.9708 22.2438 26.0 0.6 25.1 0.5 24.0 0.4 21.3 0.1 19.9 0.1 2.8 1.4588848900474078591 236.0793 0.2772 23.9 0.7 25.3 0.5 24.0 0.5 21.2 0.1 19.6 0.1 2.7 1.6588017991777322253 236.1821 6.6733 24.7 1.4 24.2 0.5 24.1 0.6 21.9 0.1 20.5 0.2 2.2 1.4587742611346949395 236.4521 11.5199 25.2 1.0 25.4 0.5 23.4 0.3 21.1 0.1 19.4 0.1 2.3 1.6587736478673405157 237.1816 8.2832 25.9 0.4 24.7 0.5 23.9 0.4 21.6 0.1 20.3 0.1 2.3 1.4588017992314717506 237.4281 6.8918 23.6 0.8 25.6 0.6 24.4 0.6 21.9 0.1 20.3 0.1 2.4 1.7587742782064231497 237.8862 61.7237 25.8 0.9 24.4 0.5 24.0 0.5 21.8 0.1 20.5 0.2 2.2 1.4587736584437237083 237.8977 27.9870 24.7 1.0 25.3 0.4 23.7 0.3 21.3 0.1 19.4 0.0 2.4 1.9587739845392270485 238.1536 15.9378 24.3 1.0 25.8 0.4 23.2 0.2 21.1 0.1 19.6 0.1 2.2 1.4587736751930147927 238.1548 34.5144 25.7 0.8 25.2 0.6 24.8 0.6 22.1 0.1 20.6 0.1 2.7 1.5587736478137124342 238.4324 7.6701 24.8 0.9 25.2 0.5 24.7 0.6 21.9 0.1 20.3 0.1 2.8 1.6587733609086452775 238.5687 46.0634 26.0 0.8 25.0 0.7 25.1 0.7 22.3 0.2 21.0 0.3 2.7 1.4587739652644734147 238.8518 21.2850 24.3 0.9 25.2 0.5 24.2 0.5 21.9 0.2 20.6 0.2 2.2 1.4587736478137386319 238.9851 7.4959 24.3 0.9 25.0 0.5 23.5 0.3 21.0 0.1 19.2 0.1 2.5 1.8588018253757678463 239.0767 37.5630 25.3 1.1 25.2 0.7 23.8 0.5 21.3 0.1 19.8 0.1 2.5 1.4587739651034514532 239.1066 19.7811 23.7 1.0 25.2 0.6 23.3 0.3 21.0 0.1 19.3 0.1 2.3 1.7587735665851958247 239.1080 42.5534 23.6 0.7 25.2 0.7 24.5 0.7 22.2 0.2 20.7 0.2 2.3 1.5587736915687245537 239.6342 8.7628 25.2 0.6 24.7 0.4 23.3 0.2 21.1 0.1 19.7 0.1 2.2 1.4

116

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587739720309343534 239.6798 18.1405 25.0 1.1 25.6 0.5 24.1 0.5 21.8 0.1 20.5 0.2 2.3 1.4587736921042388393 240.0317 30.7710 25.6 0.5 24.7 0.4 25.1 0.5 22.5 0.2 20.8 0.1 2.6 1.7587736545780958737 240.4654 3.7250 24.6 1.0 25.0 0.5 23.6 0.3 21.0 0.1 19.7 0.1 2.5 1.4588011218609374239 241.1320 47.0361 23.6 0.6 23.9 0.3 25.1 0.6 21.9 0.1 20.5 0.2 3.2 1.4587736619325261027 241.3784 26.7038 25.0 0.7 25.3 0.5 23.7 0.4 21.4 0.1 19.8 0.1 2.3 1.6588018056733459669 241.4014 36.8108 24.2 0.8 24.3 0.4 24.1 0.4 21.9 0.1 20.4 0.1 2.2 1.5587739382071231978 241.6125 21.9298 25.2 0.8 24.3 0.4 25.1 0.5 22.9 0.3 21.1 0.2 2.3 1.8587736543103616588 241.8496 6.0972 24.7 0.8 24.6 0.5 24.3 0.4 22.0 0.1 20.6 0.2 2.2 1.4587742610275763654 241.9947 9.2120 25.9 0.7 25.6 0.5 25.0 0.7 22.6 0.2 20.6 0.2 2.4 2.0587742615099475377 242.0435 13.8276 25.8 0.6 25.3 0.6 23.7 0.4 21.3 0.1 19.8 0.1 2.4 1.5587736478675633759 242.1584 7.3265 24.6 0.8 25.4 0.5 24.6 0.6 22.4 0.2 21.1 0.2 2.2 1.3588018055660438849 242.1775 35.0422 25.1 0.9 25.4 0.5 24.3 0.5 22.1 0.1 20.5 0.1 2.3 1.6587745969465197834 242.2062 18.6575 25.7 0.6 25.4 0.4 24.3 0.6 21.6 0.1 20.0 0.1 2.7 1.6587735743153964425 242.3917 30.4111 24.6 0.8 25.1 0.4 24.9 0.5 22.2 0.1 20.8 0.2 2.7 1.4587742062170867072 242.4613 13.0901 24.2 0.9 24.7 0.5 24.7 0.6 21.8 0.1 20.3 0.1 2.9 1.5588017991780140686 242.5729 5.7330 25.3 1.1 25.5 0.6 25.1 0.6 22.7 0.3 20.7 0.2 2.4 2.0587733398108570644 242.7150 36.9276 23.4 0.7 25.6 0.6 24.7 0.8 21.8 0.1 20.3 0.2 2.9 1.5587733411530540062 242.8266 37.5447 25.2 1.1 25.7 0.6 24.7 0.7 21.6 0.1 20.3 0.2 3.1 1.3587736975277753681 243.0262 21.3412 25.0 0.9 25.3 0.5 25.0 0.4 22.8 0.2 20.9 0.2 2.3 1.9587735665853990030 243.3169 39.3194 24.5 0.9 24.4 0.4 23.4 0.3 21.2 0.1 19.9 0.1 2.1 1.4588017704031618682 243.3674 6.9732 23.6 0.9 24.4 0.4 24.9 0.7 21.8 0.1 19.9 0.1 3.1 1.9588017990706922819 243.6486 4.6922 25.3 1.2 25.3 0.6 24.3 0.7 22.0 0.2 20.7 0.2 2.3 1.4587733410457519145 243.7203 35.9499 25.3 1.2 24.7 0.6 25.1 0.6 21.9 0.1 20.5 0.1 3.2 1.4587742610276550453 243.7307 8.7167 24.5 1.2 25.5 0.5 23.9 0.5 21.3 0.1 19.7 0.1 2.6 1.6587729227154129885 243.9273 49.8892 26.2 1.0 26.1 0.5 24.0 0.7 21.8 0.1 19.8 0.1 2.2 2.0588017990707054071 244.0028 4.6171 24.9 1.5 23.8 0.3 24.7 0.7 22.1 0.1 20.5 0.1 2.6 1.6587733603729540496 244.0163 40.8852 24.5 1.1 24.4 0.4 24.2 0.3 21.8 0.1 20.2 0.1 2.4 1.5

117

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

588017978915816840 244.0491 23.3466 24.1 0.7 25.2 0.4 23.7 0.8 21.1 0.1 19.6 0.1 2.6 1.5587742645701707491 244.1075 12.2334 25.1 0.9 25.1 0.5 24.0 0.4 21.6 0.1 20.2 0.1 2.3 1.4587739384742544637 244.2294 19.1452 23.6 0.9 25.0 0.6 23.6 0.4 21.5 0.1 19.5 0.1 2.1 2.0587742628534551977 244.5379 9.2653 24.6 1.6 24.9 0.7 24.1 0.6 21.2 0.1 19.8 0.1 2.9 1.5587733604266476986 244.6289 41.1774 24.8 0.8 24.8 0.4 23.3 0.2 21.1 0.1 19.7 0.1 2.2 1.4587736542031251048 244.7886 4.7700 26.1 0.4 24.5 0.4 24.3 0.5 22.1 0.1 20.6 0.2 2.2 1.5587739815318848801 244.9110 18.0632 26.0 0.6 24.9 0.5 24.0 0.4 21.7 0.1 19.8 0.1 2.3 1.9587736477603203007 245.1129 6.0467 25.1 0.8 24.8 0.5 25.1 0.5 22.0 0.1 20.2 0.1 3.1 1.8587742550692071086 245.3298 10.1221 24.0 0.8 25.2 0.4 24.2 0.4 22.0 0.1 20.4 0.1 2.2 1.6587739720848770485 245.3571 15.9546 24.6 1.3 25.0 0.6 23.6 0.4 21.5 0.1 20.0 0.1 2.2 1.4588017978916472499 245.5021 22.5628 23.6 0.5 24.7 0.3 24.0 0.3 21.8 0.1 20.4 0.1 2.2 1.3587733411531981933 245.7252 35.3316 23.1 0.6 24.8 0.6 24.8 0.6 21.9 0.1 20.5 0.2 2.8 1.4587733441588954429 246.0699 37.4823 25.0 0.8 25.1 0.4 23.3 0.2 20.8 0.0 19.4 0.1 2.5 1.5587739827678545312 246.3828 13.6807 23.1 0.6 24.9 0.6 24.5 0.7 21.5 0.1 20.1 0.1 3.0 1.4587736981712339898 246.5739 54.2199 22.8 0.6 25.1 0.7 24.7 0.7 22.4 0.3 20.5 0.2 2.3 1.8587729652884440235 246.7736 42.0935 25.3 0.9 24.4 0.5 24.4 0.6 21.4 0.1 20.0 0.1 3.0 1.4587729653957723430 246.8709 43.4958 24.6 1.0 24.8 0.6 23.5 0.3 21.3 0.1 20.0 0.1 2.1 1.3587729751668950320 247.0348 41.4821 23.3 0.5 25.1 0.5 24.0 0.4 21.3 0.1 19.9 0.1 2.7 1.4587739166239753205 247.2699 19.6234 24.7 1.5 25.1 0.8 24.4 0.9 21.8 0.2 20.4 0.2 2.6 1.4587736813139854969 247.5860 7.0929 24.3 1.3 25.4 0.6 24.8 0.6 22.1 0.1 20.6 0.2 2.8 1.5587729751669278024 247.7063 40.8164 24.6 0.9 24.8 0.5 23.4 0.3 21.0 0.1 19.7 0.1 2.3 1.3587735743156717021 247.9481 26.3187 23.8 0.6 25.2 0.5 24.8 0.5 22.4 0.2 21.0 0.2 2.4 1.4587736919436166489 248.1066 23.6474 25.3 1.1 24.7 0.5 24.5 0.5 22.3 0.2 20.6 0.1 2.2 1.7587733440516916637 248.3485 33.9695 24.6 0.9 25.3 0.4 24.8 0.5 22.5 0.2 20.9 0.2 2.3 1.7587736751935325329 248.6440 26.9571 24.6 1.3 25.5 0.6 24.4 0.6 22.1 0.2 20.6 0.2 2.3 1.5587736782000162004 248.9315 26.9147 23.7 1.0 25.5 0.7 23.8 0.5 21.0 0.1 19.1 0.1 2.8 1.9758879715545319438 248.9442 -5.1978 23.5 0.8 23.8 0.4 23.3 0.3 20.9 0.1 19.3 0.1 2.4 1.6

118

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587733441590724022 249.3206 34.4546 24.8 0.8 24.9 0.4 23.5 0.3 21.0 0.0 19.1 0.0 2.6 1.9587729652885816245 249.4168 39.6499 24.7 1.0 25.1 0.5 25.2 0.6 22.1 0.2 20.8 0.2 3.2 1.3587742782068950343 249.4335 52.7792 25.3 1.0 24.4 0.4 24.3 0.5 21.3 0.1 19.9 0.1 3.0 1.4587736751935718633 249.4523 26.2625 24.3 1.2 24.5 0.5 25.0 0.6 22.6 0.2 20.8 0.2 2.4 1.8758879663465040338 249.4910 -6.4353 24.5 1.3 24.5 0.5 24.7 0.6 21.7 0.1 20.1 0.1 3.0 1.5587736946812651159 249.5874 23.8315 25.3 0.6 25.7 0.4 25.1 0.5 22.9 0.3 21.0 0.2 2.2 1.9587733431921345875 249.6904 30.5633 25.4 0.9 24.5 0.4 24.0 0.5 21.7 0.1 20.3 0.1 2.2 1.4587739845397514242 249.7283 11.5006 25.3 0.8 24.6 0.5 25.1 0.5 22.0 0.1 20.4 0.2 3.1 1.6587739707961902675 250.2695 13.8930 23.9 1.2 25.0 0.7 24.0 0.5 21.7 0.1 20.2 0.2 2.2 1.5758879662928890205 250.6202 -7.6837 24.6 1.3 24.5 0.5 24.9 0.7 22.4 0.2 20.8 0.2 2.5 1.6587736976891774814 250.6440 18.2724 25.0 0.7 24.5 0.4 23.5 0.2 21.1 0.1 19.4 0.0 2.4 1.7587729231979742631 250.7657 44.0368 25.2 0.7 25.2 0.5 24.8 0.6 22.1 0.1 20.3 0.1 2.7 1.8588017978382681775 251.3875 18.0645 24.6 0.7 25.0 0.4 24.7 0.5 22.2 0.2 20.7 0.2 2.5 1.5758879663466088597 251.4277 -7.8792 24.8 1.3 25.1 0.6 25.6 0.5 22.3 0.2 20.4 0.2 3.2 1.9588018056202028389 251.5395 27.8247 25.5 0.8 25.5 0.4 24.9 0.5 22.2 0.1 20.5 0.2 2.7 1.7587736753546986772 251.6243 26.1073 24.1 0.9 24.7 0.5 24.2 0.5 21.9 0.1 20.5 0.1 2.3 1.4587739706889012739 251.6538 12.3188 23.1 0.8 24.1 0.5 24.1 0.7 21.7 0.1 20.3 0.2 2.3 1.4587736619330438661 251.7312 19.8500 24.9 0.8 25.1 0.5 25.0 0.5 22.3 0.2 20.6 0.1 2.7 1.7587739720851982082 252.0974 12.7373 25.4 1.0 24.5 0.5 24.3 0.5 22.0 0.2 20.6 0.2 2.3 1.5587736586054468875 252.2020 20.3096 25.3 0.7 24.9 0.6 23.6 0.4 21.0 0.1 19.7 0.1 2.5 1.4587736980105659250 252.4118 45.8986 24.4 1.0 24.5 0.5 24.2 0.4 22.1 0.1 20.3 0.1 2.1 1.8587725993039037495 252.4292 41.6562 25.7 0.8 24.6 0.5 24.2 0.6 21.1 0.1 19.7 0.1 3.1 1.4587733603734193524 252.4306 32.8219 23.8 0.9 25.7 0.5 23.7 0.3 21.5 0.1 20.1 0.1 2.1 1.4587735743695947666 252.6627 23.0738 25.2 0.8 25.0 0.4 25.1 0.5 22.1 0.1 20.7 0.2 2.9 1.4587735665322427744 252.6977 29.8417 23.9 0.7 24.9 0.5 24.4 0.6 21.2 0.1 19.8 0.1 3.2 1.4588007004197422275 252.7092 38.3522 25.1 0.8 25.5 0.5 23.7 0.4 21.3 0.1 20.0 0.1 2.4 1.3587733603734521243 252.9105 32.0392 25.5 0.9 24.1 0.4 23.4 0.3 20.8 0.1 19.2 0.1 2.6 1.6

119

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587739863639262265 252.9721 52.0506 25.5 0.8 24.8 0.5 23.9 0.4 21.4 0.1 20.0 0.1 2.5 1.4587736976356214727 253.0261 16.0940 24.9 0.9 26.1 0.3 24.4 0.4 22.0 0.1 20.4 0.1 2.3 1.6587725994112648394 253.2654 42.3323 24.9 1.1 25.6 0.5 24.6 0.7 21.8 0.2 20.4 0.2 2.8 1.4587742783680611670 253.2765 51.3818 25.1 0.7 25.1 0.4 24.7 0.6 22.3 0.2 20.9 0.2 2.3 1.5587725489986733093 253.2858 62.1073 25.4 0.8 24.8 0.7 23.5 0.4 20.9 0.1 19.5 0.1 2.6 1.4587736919439181090 253.8167 19.2425 25.5 1.2 25.7 0.7 25.0 0.9 22.8 0.3 20.6 0.2 2.2 2.2587736919439312192 253.9703 19.0003 24.1 1.7 23.8 0.3 24.9 0.9 21.9 0.1 20.4 0.1 3.1 1.5588018090551084753 254.0996 21.3105 23.2 0.5 25.0 0.5 25.1 0.5 22.0 0.1 20.5 0.2 3.1 1.5587729752746427740 254.2227 35.0509 25.4 0.6 24.8 0.5 24.8 0.5 22.5 0.2 20.9 0.2 2.4 1.6588007005271754255 254.4336 37.5274 25.2 0.7 24.7 0.4 24.9 0.5 22.6 0.2 21.3 0.3 2.2 1.4588018055130384012 254.4947 23.8064 25.4 0.8 24.6 0.4 25.0 0.5 22.4 0.1 20.8 0.2 2.7 1.5587736586055714227 254.5579 18.4856 25.0 0.8 25.3 0.5 24.0 0.5 21.0 0.1 19.5 0.1 3.0 1.5588007005271819804 254.5623 37.4297 24.0 0.7 24.9 0.5 24.9 0.5 22.0 0.1 20.5 0.2 3.0 1.4587739848072365482 254.7056 41.8400 25.1 1.1 24.5 0.6 24.5 0.5 22.2 0.2 20.3 0.1 2.3 1.9587742781535684101 254.9394 45.4067 25.3 0.8 24.9 0.6 24.2 0.5 21.9 0.1 20.2 0.1 2.3 1.7587736618795468652 255.0328 16.8106 23.9 0.9 24.8 0.6 24.2 0.4 22.0 0.1 20.5 0.1 2.2 1.5587736945742382695 255.3519 18.0737 24.5 1.0 24.3 0.4 24.1 0.5 21.1 0.1 19.7 0.1 3.0 1.4587730842593919931 255.4256 75.2287 25.6 0.7 25.3 0.6 24.8 0.6 22.1 0.1 20.5 0.1 2.7 1.6758882760135739040 255.5078 11.5037 23.1 0.8 25.5 0.6 25.3 0.7 21.9 0.2 20.6 0.3 3.4 1.4587742837363049620 255.5588 44.5236 26.1 0.5 24.3 0.6 23.5 0.4 20.9 0.1 19.1 0.1 2.6 1.8588018090015262523 255.7956 19.2954 24.5 0.9 25.4 0.5 25.0 0.6 22.5 0.2 21.1 0.3 2.4 1.4587733604809508269 255.8353 30.3520 26.4 0.4 25.7 0.4 24.1 0.5 21.9 0.1 20.4 0.2 2.2 1.5587736980644496959 255.8479 42.1073 24.6 1.0 24.9 0.5 24.1 0.4 21.9 0.1 20.5 0.2 2.2 1.3588018253229852213 255.8540 22.7398 24.8 1.2 25.2 0.6 25.0 0.7 22.0 0.2 20.5 0.2 2.9 1.5587736945742710257 255.9018 17.5926 24.9 1.0 24.4 0.4 24.3 0.5 22.0 0.1 20.4 0.1 2.3 1.6587729751137716155 255.9747 30.7506 24.4 0.9 25.2 0.5 24.0 0.4 21.9 0.1 20.5 0.1 2.1 1.4587739862031861165 256.1489 44.8678 25.3 0.9 25.3 0.4 24.5 0.5 21.9 0.1 20.6 0.2 2.6 1.4

120

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587729781199799884 256.1800 33.6150 23.7 0.8 25.6 0.4 24.7 0.5 21.9 0.1 20.5 0.1 2.8 1.4587729409155925388 256.5650 35.3264 23.8 0.7 24.6 0.5 24.4 0.6 22.3 0.2 20.9 0.2 2.2 1.4758879771378845842 256.6357 11.7766 26.0 0.5 25.6 0.5 24.8 0.6 21.9 0.1 20.5 0.1 2.9 1.5588018253766985235 256.6869 22.5763 24.9 1.3 24.0 0.4 24.4 0.7 21.4 0.1 19.6 0.1 3.0 1.8587739850219849059 256.6912 42.5799 26.2 0.4 24.8 0.5 24.2 0.5 21.8 0.1 20.2 0.1 2.5 1.5587736752476587872 256.7066 20.0545 25.2 0.9 25.6 0.5 24.6 0.6 22.3 0.2 21.0 0.2 2.2 1.4758879771915716733 256.7997 12.0263 25.9 0.8 25.0 0.5 24.8 0.6 22.3 0.2 20.9 0.2 2.5 1.4587725491597870175 256.8440 61.5855 25.4 0.9 24.6 0.5 24.0 0.5 21.8 0.2 20.5 0.2 2.2 1.4587729409156253046 256.9946 34.7249 24.3 0.8 24.5 0.5 23.6 0.4 20.9 0.1 19.5 0.1 2.7 1.4587725489989026939 257.1205 57.2346 25.9 0.5 24.3 0.6 25.1 0.7 22.1 0.2 20.5 0.2 3.0 1.6587730842058425492 257.2105 72.1206 24.6 1.2 24.7 0.5 24.6 0.6 22.3 0.2 21.0 0.2 2.3 1.4587733398653502709 257.3226 23.5716 25.9 1.1 25.6 0.7 24.3 0.9 22.0 0.2 20.2 0.2 2.3 1.8587729781200717393 257.4297 31.7636 25.0 1.0 24.4 0.4 24.9 0.5 22.0 0.1 20.6 0.1 2.9 1.4758882760673462010 257.4823 11.0434 25.2 1.2 25.0 0.8 24.3 0.7 22.0 0.2 20.7 0.2 2.3 1.4758882759599916688 257.5127 10.2060 25.9 0.8 24.7 0.7 24.2 0.7 21.7 0.2 20.2 0.2 2.5 1.5587739850220438969 257.5187 41.2803 25.9 0.5 24.8 0.5 24.4 0.5 22.3 0.2 20.6 0.1 2.1 1.7758882758526371526 257.5470 9.1500 25.1 1.4 25.5 0.9 24.6 0.9 21.6 0.2 20.1 0.1 3.0 1.5587733431926130522 257.6034 22.1850 23.9 0.5 25.2 0.5 23.9 0.4 21.1 0.1 19.6 0.1 2.8 1.5587746214818612526 257.7310 36.2683 25.8 1.0 24.3 0.5 23.6 0.4 21.0 0.1 19.7 0.1 2.6 1.3587736980109329796 257.7816 38.6284 24.6 0.9 25.2 0.5 23.7 0.4 21.5 0.1 20.2 0.1 2.2 1.4587725491598591049 257.9375 59.9488 24.9 1.1 25.1 0.6 24.5 0.6 21.7 0.1 20.3 0.2 2.8 1.4587742632274429117 258.1832 42.0965 26.1 0.6 24.5 0.5 24.9 0.7 22.5 0.2 21.0 0.2 2.4 1.5587746214282396851 258.1880 34.6982 25.1 1.3 24.6 0.6 23.9 0.6 21.1 0.1 19.8 0.1 2.8 1.4587729409157236396 258.2269 32.7377 25.8 0.5 25.2 0.5 24.7 0.6 22.5 0.2 21.0 0.2 2.3 1.4758882759063504941 258.3772 9.3276 25.6 1.2 25.5 0.7 24.5 0.9 22.1 0.2 20.6 0.2 2.5 1.4587733604811409067 258.5882 26.7106 25.3 1.1 23.6 0.3 23.8 0.4 21.6 0.1 20.2 0.1 2.2 1.4587729652355368489 258.6758 27.2485 26.0 0.6 24.7 0.6 23.6 0.4 21.4 0.1 19.8 0.1 2.3 1.5

121

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

758882760674183086 258.9452 10.2856 25.1 1.2 24.6 0.7 24.5 0.8 21.9 0.2 20.3 0.1 2.5 1.6587729782275049006 259.1334 31.0371 25.4 0.8 24.3 0.4 24.6 0.5 22.5 0.2 21.0 0.3 2.1 1.4758882758527092812 259.1883 8.4838 26.8 0.3 25.3 0.9 24.9 0.8 22.1 0.2 20.6 0.2 2.8 1.5587739849149187654 259.5068 35.7880 23.0 0.5 25.6 0.5 24.4 0.5 22.1 0.1 20.8 0.2 2.3 1.3587742632275412364 259.5289 40.0295 24.9 1.1 24.4 0.5 25.6 0.5 22.5 0.2 21.1 0.2 3.1 1.4587742633348367682 259.6630 42.0777 25.4 0.8 25.6 0.5 24.8 0.7 22.4 0.2 21.0 0.2 2.4 1.4587742632275608757 259.7201 39.6730 23.3 0.6 24.7 0.5 23.9 0.5 21.0 0.1 19.4 0.1 2.9 1.5587729751677143147 259.7740 26.0275 24.9 0.8 24.8 0.4 24.3 0.4 21.9 0.1 20.6 0.1 2.4 1.3587739850222536105 259.9737 36.9954 25.4 0.7 25.8 0.4 24.4 0.5 22.2 0.2 20.7 0.2 2.2 1.5587729652892829434 259.9849 26.2638 23.3 0.6 25.3 0.6 23.8 0.5 21.5 0.1 20.1 0.1 2.4 1.4758882761211381701 259.9916 10.4703 22.9 0.7 25.6 0.7 24.3 0.7 21.4 0.1 20.0 0.1 2.9 1.4758879770843744759 260.1522 9.6868 22.4 0.3 25.4 0.6 24.9 0.6 21.9 0.1 20.5 0.2 3.0 1.4758879770307005127 260.2121 9.0591 26.0 0.7 24.5 0.5 25.0 0.6 22.2 0.2 20.2 0.1 2.9 2.0587729408622397293 260.3897 28.4186 24.8 0.9 25.3 0.5 23.6 0.4 21.0 0.1 19.4 0.1 2.6 1.6587739863108355554 260.6001 39.5375 25.3 0.8 25.0 0.5 23.9 0.4 21.5 0.1 20.0 0.1 2.4 1.5588011502062404545 260.7412 70.5535 24.1 1.4 23.6 0.4 24.1 0.6 21.5 0.1 20.2 0.2 2.6 1.3587729781203208138 260.7426 26.8782 23.4 0.6 24.9 0.6 23.8 0.4 21.3 0.1 19.8 0.1 2.5 1.5758882758527879636 260.7825 7.6438 23.6 0.9 25.4 0.8 25.2 0.7 22.3 0.2 20.5 0.2 2.9 1.8758882760675035440 260.7964 9.5815 25.1 1.1 25.4 0.6 25.3 0.7 22.1 0.2 20.7 0.2 3.3 1.4587729408086182141 260.8324 26.8894 24.4 0.7 24.6 0.5 24.7 0.6 22.1 0.1 20.6 0.1 2.6 1.5758879769233853381 261.1184 7.7240 26.1 0.6 25.5 0.8 24.1 0.6 21.9 0.1 20.4 0.1 2.2 1.5587729408086378539 261.2006 26.5870 24.2 0.7 24.7 0.5 24.5 0.6 22.2 0.2 20.5 0.1 2.3 1.7587729781740144448 261.2399 26.9407 23.9 0.8 24.0 0.4 24.6 0.6 22.0 0.1 20.6 0.2 2.6 1.3587725491064931490 261.2604 52.8318 24.5 0.9 26.0 0.4 24.1 0.6 21.9 0.2 20.4 0.2 2.2 1.5587729408086837186 261.7103 25.7472 23.7 0.6 25.1 0.5 24.5 0.6 21.7 0.1 20.3 0.1 2.8 1.4587746215358432840 261.7363 30.4520 24.1 1.1 25.3 0.6 25.8 0.8 22.5 0.3 20.8 0.2 3.3 1.7587742632277640802 261.9570 35.2503 25.5 0.8 24.0 0.3 25.0 0.6 22.3 0.2 20.8 0.2 2.8 1.5

122

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

587746214285739793 262.2928 27.8783 25.9 0.6 25.5 0.5 25.1 0.6 22.4 0.2 20.9 0.2 2.7 1.5587739850224633642 262.3707 32.6224 22.8 0.4 24.5 0.4 24.2 0.4 21.3 0.1 19.8 0.1 2.9 1.5587725577499116558 262.3744 59.8877 24.4 1.4 24.5 0.6 24.2 0.4 22.0 0.2 20.5 0.2 2.3 1.5758877291036084359 262.9636 25.3941 25.3 0.7 25.4 0.7 23.8 0.4 21.4 0.1 19.9 0.1 2.4 1.5758882760139344771 263.1063 7.9430 24.2 1.4 25.0 0.7 24.6 0.7 21.6 0.1 20.1 0.2 3.1 1.5758882758529125574 263.3234 6.3313 25.4 1.1 25.6 0.9 23.6 0.4 21.2 0.1 19.7 0.1 2.4 1.5587739862038087456 263.3453 31.8399 24.7 1.0 24.7 0.5 24.5 0.5 22.1 0.1 20.7 0.2 2.4 1.4758882761213086475 263.5151 8.7344 25.1 1.4 25.9 0.6 24.8 0.7 22.5 0.3 20.5 0.2 2.3 2.1587742633352103738 263.5610 34.1023 23.6 0.6 24.6 0.5 25.1 0.5 22.6 0.2 21.1 0.2 2.6 1.4758877273857657029 263.6971 25.2289 25.3 0.8 25.1 0.7 25.5 0.5 22.5 0.2 20.9 0.2 3.0 1.7587742633352300273 263.6975 33.6899 23.7 0.7 24.5 0.5 25.0 0.6 22.4 0.2 21.0 0.2 2.6 1.4758877292110088500 263.8506 25.8400 24.6 0.9 25.2 0.5 23.4 0.3 21.0 0.1 19.5 0.1 2.4 1.5587742632279541546 263.9289 31.3187 24.2 0.8 25.5 0.5 24.8 0.5 21.8 0.1 20.3 0.1 2.9 1.6758877275468532229 264.8312 26.2702 25.5 0.7 25.1 0.5 24.5 0.6 22.3 0.2 20.9 0.3 2.2 1.4758877276542208313 264.9979 27.2111 25.3 0.8 25.1 0.5 23.7 0.4 21.2 0.1 19.8 0.1 2.5 1.4587734174952326699 265.1735 49.7183 24.9 1.2 25.1 0.6 24.6 0.3 22.1 0.1 20.4 0.1 2.5 1.7758877291037002069 265.2069 24.7046 25.2 0.8 25.9 0.6 23.6 0.3 21.1 0.1 19.6 0.1 2.6 1.5587734175489459584 266.0173 49.1882 24.5 0.9 25.0 0.5 23.8 0.4 20.8 0.0 19.2 0.0 3.0 1.7587730842601129417 266.3485 59.3150 24.0 0.8 24.5 0.5 24.1 0.4 21.4 0.1 20.1 0.1 2.7 1.3587734176026527402 266.9295 48.8554 25.1 0.9 25.4 0.5 25.1 0.6 22.5 0.2 21.1 0.3 2.7 1.4587734174955341054 267.1264 42.9341 25.5 1.1 25.5 0.9 24.0 0.6 21.3 0.1 19.8 0.1 2.7 1.5587730807702357170 267.3163 41.1764 24.4 1.7 26.0 0.6 23.8 0.7 21.6 0.1 20.1 0.1 2.2 1.6758877293185140800 267.3254 25.7639 24.9 0.9 25.0 0.5 24.6 0.6 21.9 0.1 20.5 0.1 2.6 1.5588011502068368684 267.4633 57.2745 23.3 0.6 25.3 0.6 24.3 0.6 22.2 0.2 20.6 0.2 2.2 1.5758883006032184816 267.8302 65.6736 23.4 0.8 25.3 0.5 24.7 0.6 21.6 0.1 20.2 0.1 3.1 1.3587734176564249664 267.9171 46.9716 25.2 0.9 24.1 0.5 23.6 0.4 21.1 0.1 19.7 0.1 2.6 1.4587730809846891561 267.9193 48.0153 25.6 1.1 24.9 0.8 23.7 0.6 21.1 0.1 19.7 0.1 2.6 1.4

123

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

758877291575052929 267.9698 24.1137 25.1 1.1 25.8 0.5 25.0 0.6 22.7 0.2 20.7 0.2 2.3 2.0588011502069810430 268.1147 54.0275 25.1 1.2 25.6 0.5 24.1 0.5 21.6 0.1 19.9 0.1 2.5 1.7758874294221145127 268.2962 78.2125 23.4 0.9 24.7 0.6 24.1 0.6 21.8 0.1 20.3 0.1 2.3 1.4588011503140930769 268.3149 59.9652 25.1 1.3 24.9 0.7 24.3 0.7 21.8 0.2 20.4 0.2 2.6 1.4758883003347961142 268.4961 63.6166 24.8 1.0 24.8 0.6 24.5 0.5 22.2 0.2 20.7 0.2 2.3 1.5587734176029869411 268.6625 41.3388 25.5 1.2 25.4 0.7 24.1 0.8 21.9 0.2 20.5 0.2 2.2 1.4758877291038575154 268.7399 23.4486 24.4 1.0 25.5 0.7 25.5 0.5 22.1 0.2 20.5 0.1 3.4 1.6587730808777082334 268.8786 39.0188 24.3 1.5 25.6 0.7 24.6 0.8 21.9 0.2 20.5 0.3 2.7 1.5588011503142372743 268.9401 56.7506 25.8 0.8 24.2 0.4 23.3 0.3 21.0 0.1 19.6 0.1 2.2 1.5587734176030459448 269.0289 39.8995 25.4 1.1 24.5 0.6 24.3 0.7 22.2 0.2 20.5 0.3 2.1 1.6758879801444206165 269.0647 44.1647 24.6 1.1 25.0 0.6 25.2 0.5 22.5 0.2 21.0 0.2 2.7 1.5758877274933562048 269.1480 24.3495 25.2 0.8 24.8 0.5 23.7 0.4 21.3 0.1 19.9 0.1 2.4 1.4588011502071776366 269.3381 49.6072 23.1 0.7 24.7 0.7 24.0 0.6 21.2 0.1 19.8 0.1 2.8 1.4758879800370595475 269.3537 43.1697 23.8 0.9 24.5 0.5 25.2 0.6 22.2 0.2 20.2 0.1 2.9 2.1587734176566937094 269.4759 40.9627 24.8 1.2 25.2 0.7 25.5 0.8 22.7 0.4 20.6 0.2 2.8 2.0588011503143290028 269.5050 54.7412 24.6 1.2 25.3 0.7 23.3 0.3 21.1 0.1 19.7 0.1 2.2 1.4758877274933758866 269.6641 24.2277 24.8 0.9 25.6 0.5 24.4 0.4 21.8 0.1 20.5 0.1 2.5 1.4758877292649450148 269.9273 24.4050 24.5 1.0 24.2 0.4 24.2 0.5 21.8 0.1 20.5 0.2 2.4 1.4758877274934086491 270.3753 24.0512 23.9 0.8 25.0 0.6 24.7 0.6 21.5 0.1 19.7 0.1 3.3 1.8588011503145452721 270.5323 49.7575 25.2 1.3 25.9 0.6 25.1 0.8 21.9 0.2 20.2 0.2 3.2 1.7758879743999608647 270.5526 42.5107 24.8 1.1 25.1 0.5 24.1 0.4 21.7 0.1 20.3 0.1 2.4 1.4758877274934217530 270.7269 23.9671 25.4 0.8 25.2 0.6 24.7 0.6 21.6 0.1 20.2 0.1 3.0 1.4588011503146042364 270.7437 48.5025 23.8 1.3 26.2 0.6 24.1 0.7 22.0 0.2 20.3 0.2 2.2 1.6758877276007959231 270.9368 24.6711 25.7 0.6 24.5 0.5 24.1 0.5 21.5 0.1 19.9 0.1 2.5 1.6758882837984248917 271.6909 64.9125 25.4 1.0 25.2 0.7 23.8 0.5 21.6 0.1 20.3 0.1 2.2 1.3758879799834708180 272.1941 42.3734 24.3 1.1 24.6 0.4 24.5 0.5 21.8 0.1 20.4 0.1 2.7 1.4758882836910703914 272.5915 64.0585 25.6 0.9 25.5 0.5 24.2 0.6 22.0 0.2 20.4 0.2 2.3 1.5

124

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

758879800371906760 273.3558 42.5621 25.2 0.8 25.1 0.5 24.1 0.5 21.9 0.1 20.5 0.1 2.2 1.4758879745611073714 273.6150 43.1534 23.9 0.7 25.2 0.4 23.8 0.3 21.4 0.1 19.5 0.1 2.3 1.9758879800372299970 274.5077 42.2531 25.4 0.8 24.5 0.5 24.4 0.5 21.6 0.1 19.6 0.1 2.8 2.0758879800372365338 274.6957 42.3814 25.6 0.7 25.1 0.6 23.9 0.4 21.3 0.1 19.8 0.1 2.6 1.5758882835837617362 275.8669 63.1277 26.0 0.7 25.2 0.8 25.0 0.8 22.2 0.2 20.7 0.2 2.8 1.5758879800372824046 276.0684 41.8951 23.3 0.6 24.8 0.5 24.8 0.6 22.2 0.2 20.7 0.2 2.6 1.5758879801983436639 276.4392 43.1702 25.8 0.9 25.3 0.5 24.5 0.6 22.0 0.2 20.6 0.2 2.5 1.3758883003886470770 276.9034 63.6557 24.5 1.2 24.5 0.5 24.2 0.5 21.7 0.1 20.3 0.1 2.5 1.4758879745075448276 276.9994 41.9097 25.2 0.8 25.2 0.4 24.1 0.4 21.4 0.1 19.8 0.1 2.8 1.5758879801983633403 277.1004 43.0152 23.6 0.9 25.3 0.5 23.9 0.5 20.9 0.1 19.2 0.0 3.0 1.7758879745075776134 278.0546 41.7461 25.4 0.7 25.3 0.4 24.1 0.4 21.5 0.1 19.7 0.1 2.6 1.8758879799299934602 278.2223 40.5655 23.8 0.9 24.4 0.6 24.4 0.6 21.7 0.1 20.3 0.1 2.7 1.4758879799300000074 278.3825 40.4587 24.6 1.2 26.0 0.6 25.6 0.5 22.6 0.3 20.5 0.1 3.1 2.1758879801447483544 278.9912 42.1108 24.9 1.1 25.1 0.6 24.9 0.6 22.5 0.2 20.9 0.2 2.5 1.5758879801984551053 279.8073 42.3506 24.5 1.4 24.9 0.6 25.1 0.6 22.1 0.2 20.7 0.2 3.0 1.4758882836376455142 285.5722 62.6958 25.0 1.5 24.8 0.5 24.3 0.6 22.1 0.2 20.5 0.1 2.2 1.6758883004961916696 285.9520 63.8609 26.2 0.6 25.1 0.5 24.8 0.5 21.5 0.1 20.1 0.1 3.3 1.5758883006035724115 286.5770 64.5230 25.7 0.9 25.7 0.4 25.2 0.6 22.8 0.3 21.0 0.2 2.3 1.9758882837987198851 287.0166 63.8325 25.3 0.8 24.2 0.4 23.6 0.3 21.2 0.1 19.6 0.1 2.4 1.6758874337169704032 288.4135 77.8720 25.7 1.0 24.7 0.7 24.0 0.7 21.8 0.2 20.4 0.2 2.1 1.5758874337706574831 288.6738 78.3016 25.6 1.1 24.5 0.7 23.8 0.6 21.6 0.1 20.2 0.2 2.2 1.4758883034478347963 289.1602 62.7378 24.3 1.3 25.3 0.6 24.0 0.5 20.9 0.1 19.5 0.1 3.1 1.3758874294759851155 289.4078 78.5075 25.7 1.2 25.2 0.7 24.0 0.7 21.2 0.1 19.8 0.1 2.8 1.4758883004425832388 289.4148 62.8697 25.4 0.9 24.5 0.5 24.5 0.5 21.4 0.1 19.9 0.1 3.1 1.5758874293686305978 289.9318 77.5889 24.1 1.4 24.5 0.6 25.2 0.9 22.2 0.2 20.5 0.2 3.0 1.6758883033404999281 290.2589 61.6931 23.9 1.0 24.5 0.7 25.1 0.6 22.1 0.2 20.8 0.2 3.0 1.3758874293149500612 290.7478 77.2522 26.5 1.0 25.1 0.8 25.1 0.9 21.9 0.2 20.3 0.2 3.2 1.6

125

Table C.1 (cont’d)

Object ID RA DEC u u err g g err r r err i i err z z err r-i i-z

758874293149828414 293.8706 76.9509 24.8 1.2 24.9 0.7 25.4 0.7 22.5 0.3 20.6 0.2 2.9 1.9758874294760899955 300.5010 77.8988 25.7 0.8 25.4 0.6 25.1 0.7 22.0 0.2 20.6 0.2 3.0 1.5

126

Appendix D

EXPANSION ON THE EXPECTED HVS CALCULATIONS.

Here we expand on the calculations outlined in section 3.6.4, determining the expected

number of HVSs originating from an interaction with a central SMBH assuming varying

initial mass functions.

We start with the Salpeter IMF, given by the equation:

dN

dM=

∫ M2

M1

M−2.35 (4.1)

where dNdM

is the number of stars in a small mass range and M1 is the lower mass limit

and M2 is the upper mass limit. If we follow exactly the prediction from Section 3.6.4,

considering the 0.6 − 1.2 solar mass range for G/K-type stars and the 3 − 4 solar mass

range for the known B-type HVS, we find:

NB

NG/K

=

∫ 4

3M−2.35∫ 1.2

0.6M−2.35

=3−1.35 − 4−1.35

0.6−1.35 − 1.2−1.35=

0.7

1.2(4.2)

Once scaled for the 14 known B-type HVS that were also detected by SDSS, we get that

the expected number of G/K-type HVS is roughly 240.

However, since we were uncertain of the exact masses for the confirmed high mass

HVS, we instead assumed an average mass of 3.5 M� to determine dNdM

, the number of

stars in a 1 dex mass bin around this average, and to be more in line with the approach of

Kollmeier et al. (2010). Similarly, at the low mass end of the IMF low mass stars dominate

127

significantly, and we assume that the contribution from 1.2 M� stars is negligible. In this

case, we find:

NB

NG/K

=3.5−1.35

0.6−1.35(4.3)

Scaling for the 14 known B-type HVSs, yields the predicted ∼150 G/K-type HVSs stated

in Section 3.6.4.

We make similar assumptions for the top-heavy IMF (Figer et al., 1999):

dN

dM=

∫ M2

M1

M−1.6 =3.5−0.6

0.6−0.6(4.4)

Assuming an average B-type mass of 3.5 M� and a dominating contribution from 0.6 M�

stars, we get the expected 40 G/K-type HVSs.

128

References

Abadi, M. G., Navarro, J. F., & Steinmetz, M. 2006, MNRAS, 365, 747

—. 2009, ApJ, 691, L63

Abadi, M. G., Navarro, J. F., Steinmetz, M., & Eke, V. R. 2003, ApJ, 597, 21

Abt, H. A. 1983, ARA&A, 21, 343

Aguerri, J. A. L., Gerhard, O. E., Arnaboldi, M., Napolitano, N. R., Castro-Rodriguez,

N., & Freeman, K. C. 2005, AJ, 129, 2585

Aihara, H., et al. 2011a, ApJS, 195, 26

—. 2011b, ApJS, 193, 29

Allende Prieto, C., Beers, T. C., Wilhelm, R., Newberg, H. J., Rockosi, C. M., Yanny,

B., & Lee, Y. S. 2006, ApJ, 636, 804

Allende Prieto, C., et al. 2008, AJ, 136, 2070

—. 2014, A&A, 568, A7

Alves-Brito, A., Melendez, J., Asplund, M., Ramırez, I., & Yong, D. 2010, A&A, 513,

A35+

An, D., et al. 2009, ApJ, 700, 523

—. 2013, ApJ, 763, 65

129

Bahcall, J. N., & Wolf, R. A. 1976, ApJ, 209, 214

Bartko, H., et al. 2010, ApJ, 708, 834

Belokurov, V., et al. 2006a, ApJ, 642, L137

—. 2006b, ApJ, 642, L137

Bensby, T., Alves-Brito, A., Oey, M. S., Yong, D., & Melendez, J. 2011, ApJ, 735, L46

Bessell, M. S., & Brett, J. M. 1988, PASP, 100, 1134

Binney, J., & Merrifield, M. 1998, Galactic Astronomy, ed. J. Binney & M. Merrifield

Bird, J. C., Kazantzidis, S., & Weinberg, D. H. 2011, ArXiv e-prints

Bird, J. C., Kazantzidis, S., Weinberg, D. H., Guedes, J., Callegari, S., Mayer, L., &

Madau, P. 2013, ApJ, 773, 43

Blaauw, A. 1961, Bull. Astron. Inst. Netherlands, 15, 265

Blanton, M. R., et al. 2003, AJ, 125, 2348

Bond, H. E. 1970, ApJS, 22, 117

Bond, N. A., et al. 2010, ApJ, 716, 1

Bournaud, F., Elmegreen, B. G., & Elmegreen, D. M. 2007, ApJ, 670, 237

Bovy, J., Rix, H.-W., & Hogg, D. W. 2012a, ApJ, 751, 131

Bovy, J., Rix, H.-W., Liu, C., Hogg, D. W., Beers, T. C., & Lee, Y. S. 2012b, ApJ, 753,

148

130

Brown, W. R., Geller, M. J., & Kenyon, S. J. 2009, ApJ, 690, 1639

—. 2012, ApJ, 751, 55

Brown, W. R., Geller, M. J., Kenyon, S. J., & Kurtz, M. J. 2005, ApJ, 622, L33

Burgasser, A. J., Cruz, K. L., Cushing, M., Gelino, C. R., Looper, D. L., Faherty, J. K.,

Kirkpatrick, J. D., & Reid, I. N. 2010, ApJ, 710, 1142

Byrd, G., & Valtonen, M. 1990, The Astrophysical Journal, 350, 89

Caldwell, N., Morrison, H., Kenyon, S. J., Schiavon, R., Harding, P., & Rose, J. A. 2010,

AJ, 139, 372

Carollo, D., et al. 2007, Nature, 450, 1020

—. 2010, ApJ, 712, 692

Chandar, R., Fall, S. M., & Whitmore, B. C. 2010, ApJ, 711, 1263

Cheng, J. Y., et al. 2012, ApJ, 752, 51

Chernoff, D. F., & Weinberg, M. D. 1990, ApJ, 351, 121

Chou, M., et al. 2007, ApJ, 670, 346

Cohen, J. G. 1978, ApJ, 221, 788

Conroy, C., Wechsler, R. H., & Kravtsov, A. V. 2007, ApJ, 668, 826

Covey, K. R., et al. 2007, AJ, 134, 2398

131

de Vaucouleurs, G. 1964, in IAU Symposium, Vol. 20, The Galaxy and the Magellanic

Clouds, ed. F. J. Kerr, 195–+

Do, T., Ghez, A. M., Morris, M. R., Lu, J. R., Matthews, K., Yelda, S., & Larkin, J.

2009, ApJ, 703, 1323

Dong, R., Gunn, J., Knapp, G., Rockosi, C., & Blanton, M. 2011, AJ, 142, 116

Durrell, P. R., Ciardullo, R., Feldmeier, J. J., Jacoby, G. H., & Sigurdsson, S. 2002, ApJ,

570, 119

Edelmann, H., Napiwotzki, R., Heber, U., Christlieb, N., & Reimers, D. 2005, ApJ, 634,

L181

Eggen, O. J., Lynden-Bell, D., & Sandage, A. R. 1962, ApJ, 136, 748

Eisenstein, D. J., et al. 2011, AJ, 142, 72

Fan, X., et al. 2001, AJ, 121, 31

Feldmeier, J. J., Ciardullo, R., Jacoby, G. H., & Durrell, P. R. 2004a, ApJ, 615, 196

Feldmeier, J. J., Mihos, J. C., Morrison, H. L., Harding, P., & Kaib, N. 2004b

Feldmeier, J. J., Mihos, J. C., Morrison, H. L., Rodney, S. A., & Harding, P. 2002, ApJ,

575, 779

Figer, D. F., Morris, M., Geballe, T. R., Rich, R. M., Serabyn, E., McLean, I. S., Puetter,

R. C., & Yahil, A. 1999, ApJ, 525, 759

Fouquet, S., Hammer, F., Yang, Y., Puech, M., & Flores, H. 2012, MNRAS, 427, 1769

132

Freeman, K., & Bland-Hawthorn, J. 2002, ARA&A, 40, 487

Freeman, K. C. 1987, ARA&A, 25, 603

Fukugita, M., Ichikawa, T., Gunn, J. E., Doi, M., Shimasaku, K., & Schneider, D. P.

1996a, AJ, 111, 1748

—. 1996b, AJ, 111, 1748

Ghez, A. M., et al. 2008, ApJ, 689, 1044

Gilmore, G. 1984, MNRAS, 207, 223

Gilmore, G., & Reid, N. 1983, MNRAS, 202, 1025

Gnedin, O. Y., & Ostriker, J. P. 1997, ApJ, 474, 223

Gould, A. 2003, AJ, 126, 472

Gould, A., & Kollmeier, J. A. 2004, ApJS, 152, 103

Gould, A., & Quillen, A. C. 2003, ApJ, 592, 935

Gould, A., & Salim, S. 2003, ApJ, 582, 1001

Gunn, J. E., et al. 1998, AJ, 116, 3040

—. 2006, AJ, 131, 2332

Gvaramadze, V. V., Gualandris, A., & Portegies Zwart, S. 2009, MNRAS, 396, 570

Harding, P., Morrison, H. L., Olszewski, E. W., Arabadjis, J., Mateo, M., Dohm-Palmer,

R. C., Freeman, K. C., & Norris, J. E. 2001, AJ, 122, 1397

133

Harris, W. E. 1997, VizieR Online Data Catalog, 7202, 0

Hawley, S. L., et al. 2002, AJ, 123, 3409

Hernquist, L. 1990, ApJ, 356, 359

Hills, J. G. 1988, Nature, 331, 687

Hirsch, H. A., Heber, U., O’Toole, S. J., & Bresolin, F. 2005, A&A, 444, L61

Hogg, D. W., Finkbeiner, D. P., Schlegel, D. J., & Gunn, J. E. 2001, AJ, 122, 2129

Holley-Bockelmann, K., Sigurdsson, S., Mihos, J. C., Feldmeier, J. J., Ciardullo, R., &

McBride, C. 2005, ArXiv Astrophysics e-prints

Ibata, R., Lewis, G. F., Irwin, M., Totten, E., & Quinn, T. 2001, ApJ, 551, 294

Ibata, R., Martin, N. F., Irwin, M., Chapman, S., Ferguson, A. M. N., Lewis, G. F., &

McConnachie, A. W. 2007, ApJ, 671, 1591

Ivezic, Z., et al. 2004, Astronomische Nachrichten, 325, 583

—. 2007, AJ, 134, 973

—. 2008, ApJ, 684, 287

Jacoby, G. H., & Ciardullo, R. 1999a, ApJ, 515, 169

—. 1999b, ApJ, 515, 169

Kauffmann, G., White, S. D. M., & Guiderdoni, B. 1993, MNRAS, 264, 201

Kilic, M., et al. 2006, AJ, 131, 582

134

King, III, C., Brown, W. R., Geller, M. J., & Kenyon, S. J. 2012, ApJ, 750, 81

Kirby, E. N., Simon, J. D., Geha, M., Guhathakurta, P., & Frebel, A. 2008, ApJ, 685,

L43

Kirkpatrick, D. in prep.

Kollmeier, J. A., Gould, A., Knapp, G., & Beers, T. C. 2009, ApJ, 697, 1543

Kollmeier, J. A., et al. 2010, ApJ, 723, 812

Krick, J. E., & Bernstein, R. A. 2007, AJ, 134, 466

Laidler, V. et al, Synphot User’s Guide, Version 5.0 (Baltimore STScI). 2005

Lang, M., Holley-Bockelmann, K., Bogdanovic, T., Amaro-Seoane, P., & Sesana, A. 2011,

ArXiv e-prints

Larson, R. B. 1969, MNRAS, 145, 405

—. 1976, MNRAS, 176, 31

Law, D. R., & Majewski, S. R. 2010, ApJ, 718, 1128

Lawrence, A., et al. 2007, MNRAS, 379, 1599

Lee, M. G., Park, H. S., & Hwang, H. S. 2010, Science, 328, 334

Lee, Y. S., et al. 2008a, AJ, 136, 2022

—. 2008b, AJ, 136, 2050

—. 2011, AJ, 141, 90

135

Leonard, P. J. T., & Dewey, R. J. 1993, in Astronomical Society of the Pacific Conference

Series, Vol. 45, Luminous High-Latitude Stars, ed. D. D. Sasselov, 239

Lokas, E. L., & Mamon, G. A. 2001, MNRAS, 321, 155

Lopez-Corredoira, M., Cabrera-Lavers, A., Mahoney, T. J., Hammersley, P. L., Garzon,

F., & Gonzalez-Fernandez, C. 2007, AJ, 133, 154

Magorrian, J., & Tremaine, S. 1999, MNRAS, 309, 447

Majewski, S. R. 1993, ARA&A, 31, 575

Majewski, S. R., Skrutskie, M. F., Weinberg, M. D., & Ostheimer, J. C. 2003, ApJ, 599,

1082

Manukian, H., Guillochon, J., Ramirez-Ruiz, E., & O’Leary, R. M. 2013, ApJ, 771, L28

Mateo, M., Olszewski, E. W., & Walker, M. G. 2008, ApJ, 675, 201

McConnachie, A. W., et al. 2009, Nature, 461, 66

McLaughlin, D. E., & Fall, S. M. 2008, ApJ, 679, 1272

Merritt, D. 1984, ApJ, 276, 26

Mihalas, D., & Binney, J. 1981, Galactic astronomy: Structure and kinematics /2nd

edition/, ed. Mihalas, D. & Binney, J.

Mihos, C. 2003, ArXiv Astrophysics e-prints

Mihos, J. C. 2004, 217, 390

136

Mihos, J. C., Harding, P., Feldmeier, J., & Morrison, H. 2005, ApJ, 631, L41

Miyamoto, M., & Nagai, R. 1975, PASJ, 27, 533

Moore, B., Katz, N., Lake, G., Dressler, A., & Oemler, A. 1996, Nature, 379, 613

Morris, M., & Serabyn, E. 1996, ARA&A, 34, 645

Morrison, H. L. 1993, AJ, 106, 578

Morrison, H. L., Mateo, M., Olszewski, E. W., Harding, P., Dohm-Palmer, R. C., Freeman,

K. C., Norris, J. E., & Morita, M. 2000, AJ, 119, 2254

Munn, J. A., et al. 2004, AJ, 127, 3034

—. 2008, AJ, 136, 895

Murante, G., Giovalli, M., Gerhard, O., Arnaboldi, M., Borgani, S., & Dolag, K. 2007,

MNRAS, 377, 2

Murante, G., et al. 2004, ApJ, 607, L83

Napiwotzki, R., & Silva, M. D. V. 2012, Mem. Soc. Astron. Italiana, 83, 272

Napolitano, N. R., et al. 2003, ApJ, 594, 172

Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490, 493

Oke, J. B., et al. 1995, PASP, 107, 375

Oort, J. H. 1958, Ricerche Astronomiche, Vol. 5, Specola Vaticana, Proceedings of a

Conference at Vatican Observatory, Castel Gandolfo, May 20-28, 1957, Amsterdam:

137

North-Holland, and New York: Interscience, 1958, edited by D.J.K. O’Connell., p.415,

5, 415

Palladino, L. E., Schlesinger, K. J., Holley-Bockelmann, K., Allende Prieto, C., Beers,

T. C., Lee, Y. S., & Schneider, D. P. 2014, ApJ, 780, 7

Palladino, L. E., et al. 2012, AJ, 143, 128

Peng, E. W., et al. 2011, ApJ, 730, 23

Pickles, A. J. 1998, PASP, 110, 863

Pier, J. R., Munn, J. A., Hindsley, R. B., Hennessy, G. S., Kent, S. M., Lupton, R. H.,

& Ivezic, Z. 2003, AJ, 125, 1559

Piffl, T., Williams, M., & Steinmetz, M. 2011, A&A, 535, A70

Poveda, A., Ruiz, J., & Allen, C. 1967, Boletin de los Observatorios Tonantzintla y

Tacubaya, 4, 86

Przybilla, N., Nieva, M. F., Heber, U., & Butler, K. 2008, ApJ, 684, L103

Quinlan, G. D. 1996, New Astronomy, 1, 35

Reid, I. N., & Hawley, S. L. 2005, New light on dark stars : red dwarfs, low-mass stars,

brown dwarfs, ed. I. N. Reid & S. L. Hawley

Reid, M. J., & Brunthaler, A. 2004, ApJ, 616, 872

Richards, G. T., et al. 2002, AJ, 123, 2945

138

Rockosi, C., Beers, T. C., Majewski, S., Schiavon, R., & Eisenstein, D. 2009, in ArXiv

Astrophysics e-prints, Vol. 2010, astro2010: The Astronomy and Astrophysics Decadal

Survey, 14–+

Rougoor, G. W., & Oort, J. H. 1960, Proceedings of the National Academy of Science,

46, 1

Rudick, C. S., Mihos, J. C., Frey, L. H., & McBride, C. K. 2009, ApJ, 699, 1518

Sadler, E. M., Rich, R. M., & Terndrup, D. M. 1996, AJ, 112, 171

Sales, L. V., Navarro, J. F., Abadi, M. G., & Steinmetz, M. 2007, MNRAS, 379, 1475

Sato, K., Tokoi, K., Matsushita, K., Ishisaki, Y., Yamasaki, N. Y., Ishida, M., & Ohashi,

T. 2007, ApJ, 667, L41

Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525

Schlesinger, K. J., et al. 2012, ApJ, 761, 160

Schmidt, S. J., West, A. A., Hawley, S. L., & Pineda, J. S. 2010, AJ, 139, 1808

Schodel, R., et al. 2007, A&A, 469, 125

Schonrich, R. 2012, MNRAS, 427, 274

Schonrich, R., & Binney, J. 2009, MNRAS, 399, 1145

Schonrich, R., Binney, J., & Dehnen, W. 2010, MNRAS, 403, 1829

SDSS-III. 2008, Massive Spectroscopic Surveys of the Distant Universe, the Milky Way

Galaxy, and Extra-Solar Planetary Systems, abstracted from an NSF proposal

139

SDSS-III Collaboration et al. 2012, ArXiv e-prints

Searle, L., & Zinn, R. 1978, ApJ, 225, 357

Sesana, A., Haardt, F., & Madau, P. 2006, ApJ, 651, 392

Sherwin, B. D., Loeb, A., & O’Leary, R. M. 2008, MNRAS, 386, 1179

Simon, J. D., & Geha, M. 2007, ApJ, 670, 313

Skiff, B. A. 2010, VizieR Online Data Catalog, 1, 2023

Smee, S. A., et al. 2013, AJ, 146, 32

Smith, M. C., et al. 2007, MNRAS, 379, 755

Smolinski, J. P., et al. 2011, AJ, 141, 89

Sohn, S. T., Anderson, J., & van der Marel, R. P. 2012, ApJ, 753, 7

Tauris, T. M. 2015, MNRAS, 448, L6

Tinsley, B. M., & Larson, R. B. 1979, MNRAS, 186, 503

http://www.sdss.org. ????

Villalobos, A., & Helmi, A. 2008, MNRAS, 391, 1806

von Weizsacker, C. F. 1951, ApJ, 114, 165

Williams, B. F., et al. 2007, ApJ, 656, 756

Worthey, G., & Lee, H. 2006, ArXiv Astrophysics e-prints

140

Yanny, B., et al. 2000, ApJ, 540, 825

—. 2009, AJ, 137, 4377

York, D. G., et al. 2000a, AJ, 120, 1579

—. 2000b, AJ, 120, 1579

Yoshii, Y., & Saio, H. 1979, PASJ, 31, 339

Yu, Q., & Tremaine, S. 2003, ApJ, 599, 1129

Zhang, F., Lu, Y., & Yu, Q. 2013, ApJ, 768, 153

Zucker, D. B., et al. 2007, ApJ, 659, L21

141